The effect of destroying "money" depends on a multitude of different factors.

Like how much are you burning, how is the money distributed within the country and outside of the country, who does the burning, how is the money used in the first place, how accepted is your currency, how does it relate to other currencies, does your country have fixed/semi-fixed prices and so on and on and on.

The thing is, it already makes a difference whether you use idk cigarettes, grain, gold or paper or labor/time vouchers/favors as money and currency. Some of those are consumables, some are naturally depleting in value, others are stable and useless, some possess an intrinsic value, some only posses an exchange value, some are naturally limited, other's are completely fungible commodities and so on.

So likely the first trades happened via a direct exchange of goods and services. So wealth was ownership of intrinsically valuable goods and services. Now destroying those would destroy intrinsic value leaving you worse off than before. Though whether that also effects other people depends on the scope of destruction (environmental damage etc), as well as on the amount of trade happening, so idk if you were the farmer and people relied on the harvest that you'd destroyed you'd disrupt the food supply of a society, while if you weren't part of a society and consumed what you produced all by yourself then your action would have no impact on anybody but yourself.

Next up might be trade via semi-fungible intrinsically valuable goods like idk grain or lifestock. Which allows you to assign a semi-objective value to them and that value is roughly the same for all people with whom you trade. Like they all need to eat, they all eat roughly the same anyway and you've no problem exchanging these goods for other goods and services as their necessity and natural depletion means they are always in high demand. So again if you burn those trade items you're effectively worse of yourself, while the effect on other people relies on how much they relied on your overproduction and the general "wealth" (access to these necessities) of that civilization.

Some problems with grain and lifestock are though that you can only use so much of those, after which their value to yourself will decrease and create work. Like you have to feed and care for your animals you have to protect your corn from the environment, your goods can spoil and die rendering them worthless and if everyone is well nutritioned their value will also decrease. Though given their natural depletion and their necessity they also mean power. Like as you can't opt out of eating, you can leverage supply and demand against other people. So let's say your society has 100 people you have 50 farmers and 50 lumber jacks and the 50 farmers produce 3 times as much as they consume. Now 1/3 is taken for themselves leaving 2 thirds for trade. Now as the lumberjacks also only need 1/3 the last 1/3 is without value. It has cost work to produce it, it would cost work to store it and you're not getting something valuable in return for it. So destroying or never creating it in the first place makes no difference to either the farmer or the group of lumberjacks (at least for now, when the next harvest is less fruitful they might think differently about it).

And I guess from there you already go towards tokens, contracts and "trust" as currency. So take the farmer and their oversupply and suppose they divide that oversupply into meal sized chucks gather as many valuable or worthless tokens as they have chunks and within a trade either allow the person to directly take their grain or accept a token for now and be able to return it for grain later. So that the value of the token is fixed to "set amount of grain". Were depending on the trust in the other person keeping their end of a contract the token is either an intrinsically valuable but easier to transport deposit or is entirely worthless and only covered by the traders reputation to honor their word.

Now destroying your token again sets you back considerably because you now have no longer the right to ask for grain, but otherwise it has no effect other than the farmer having grain that no one comes to claim and which they might claim for themselves. Now a side effect is that both the grain and the token are fungible so the farmer could give out old grain first and prevent his supply from rotting, while the token owner could also use any such token or could also trade that token for something else which they deem worth as much. Again probably the latter at first also needed to come with contracts or a system of trust in both the trader and the farmer to accept the token without their original owner and so on.

Now after that system a considerable problem arises with the choice of the tokens because either you're talking about personalized tokens which are non-fungible and hard to trade with others (like you'd still need to regularly come to that one farmer to do the actual exchange) or they are too fungible and people could just replicate a token an grab the amount of grain without having exchanged anything useful for it (worthless token for valuable grain).

So the more fake tokens the lesser you have a chance to get any grain if you don't come early so destroying excess supply might even do people a favor as otherwise either the whole trust based system collapses or the value of a token decreases (idk less grain to supply everyone with a token or stuff like that).

Now the more accepted such a token system gets and the higher the trust, the lower the physical value of the token can become and so that it doesn't have to be a deposit anymore to be valuable. So in a sense this can become political, because now the value of that token is no longer in itself, no longer in the thing that it can be exchanged for or the trust in a single entity, but it's a system of trust. It's the executive branch and/or juridical branch of that countries government that upholds rights to tokens, criminalizes theft and forgery and enforces that contracts are honored. So a state apparatus can become the backbone of this system of trade and it can become the self-interest of the upper and middle classes to uphold a system of government because their legal, executive and juridical power can mark the difference between "being rich" and owning a bunch of worthless trash.

And over time the "backup" of that trust based token system has more and more shifted from (the token supplier) owning a large stock of stuff that you can exchange their tokens for, to holding a large pile of gold that serves as security for your money, but which is rarely if ever requested as such, to not having a security for that money at all. So as of right now money is effectively completely worthless and only backed by the fact that other people actually buy into that system and TREAT it as valuable.

On top of that banks have moved from a "positive" stock as the source of their tokens to a "negative" stock. So previously you might have had tons of grain and gave out tokens according to the grain you had in your vault. But nowadays banks don't really have that much currency in their vaults. They have a limited amount to supply everyday people with cash if requested, but not in excessive quantities and far less than those people have in their bank accounts. So if there ever was a bank run where everyone tried to get their money, the banks would be in trouble because they actually give out more money than they actually have.

So if they have 10 tokens worth of grain they might give out 100 tokens worth of grain hoping that only ever 10 people at a time will actually want the grain and not just a token. And as credits, if successfully repaid, bring in more money than they initially requested, banks might actually turn a profit with that, where over time they have the money that they lent to other people despite the fact that they did not having it when they actually lent it to these people. In the process they might end up "creating money", because their credits might supply more money than what is available in cash (and that was already a worthless quantity).

So the either you have to move to a completely digital or book keeping business (old school blockchain) or you have to print new cash to keep up with this kind of inflation of money and currency. So burning cash might not so much be an economical problem but a logistical problem as you'd require access to cashless payment options anywhere otherwise you'd technically have the money but no means to transfer it.

Also hoarded cash, not repaid credits, giving out too many credits, forgery and fraud etc, can all seriously disturb the economy as technically the backup for the money is the market in which it is used, but these things can suddenly increase or decrease the available amount of money and as such mess with supply, demand, prices and the value of the currency.

All while giving out credit and the potential of funding approaches that might produce that surplus that is necessary to repay the credit interest rates is what is keeping the market growing, which repays that credits and bridges the gap between imaginary money and real world goods with intrinsic value and as such serves as backup for the entire currency.

So in a sense money is a stake in the economy of the domain which uses that currency. And as such it is a zero-sum game. If there are hundred goods and 100 shares in owning these goods and you'd burn yours then the remaining 99 shares would still correspond to 100 goods so the value of 1 share increased from 1 to 1 + 1/99. Though what that also means is that it's just a matter of distribution of stuff, you're not actually destroying anything, by adding or subtracting money you just change the wealth of different people.

So again if previously everyone owned 1/100 of the total money supply and I print 100 more bills, then suddenly I have half of the claim to all the stuff (100 out of 200) while anybody else has half of their original claim (from 1 of 100 to 1 of 200).

Though if I were to own that much money or even "all the money" I'd suddenly be incredibly poor because there's nothing stopping people from just not accepting and using the currency that I own, but instead trade in something else. Like if you owned all the dollars people could trade in cigarettes, bottle caps or Dollar2.0 or whatever weird cryptocoin is currently the hype. Again the value of the currency is derived from the fact that people treat it as having any value at all.

Which opens up another angle for that, which is expansion of the domain of trade. So is it worth for people to join the trading system of a country and accept it's currency, risking that they increase the money supply and thus decrease the value of the currency that you hold or that they decrease the money supply and make you a larger owner of their economy or what if they suddenly change the currency to something else defrauding you entirely?

Also while technically possible, it's an incredibly risky move because after all, the entire system is kinda based on trust and/or power so doing such a move and risking hiccups of the economy can be seen as an assault on another countries economy and their well being, leading to diplomatic, political and even military struggles. Being able to control supply and demand to direct streams of goods and services is power over one or even many societies and as such a vital political issue.

So TL;DR it depends...