Taking small amounts till there's nothing left

A specific type of this scenario can be called the tragedy of the commons, in which self-interested individuals rationally and reasonably avail themselves of a common good, but the net effect is overuse which destroys the good for everyone. The term comes from the metaphor of a common pasture which is available for anyone to graze their cows, but if everyone does so, the pasture will become barren and worthless. A key to this type of scenario is that each individual has a rather small effect, that no individual is better served by refraining from the behavior, but that they'll all be doomed if they practice it, ultimately leading to a situation where no one has an incentive to stop, and inevitable tragedy unless something is done.

1. Nibbled to death by ducks

2. Pecked to death by a hen

3. Death by a thousand cuts

Idiom 3 might a bit too harsh for your purposes as it comes from an actual Chinese/East Asian method of torture-execution.

Idioms 1 and 2 aren't very common today but have been around since at least 1737 (John Ray, A Compleat Collection of English Proverbs, p. 186):

One had as good be nibbled to death by ducks,or,pecked to death by a hen.

Modern uses of 1. Nibbled to death by ducks:

Joan Didion (The Year of Magical Thinking, 2005):

"I warned you," John said. "I told you what working for Life would be like. Didn't I tell you? It would be like being nibbled to death by ducks?"

Laura McCullough (chair of a Physics department, 2011):

“Nibbled to death by ducks.” The phrase, though nearly three centuries old, is still remarkably apt for the role of the department chair today. Our jobs are filled with little nibbles taken out of our time and attention; no individual nibble may be all that significant, but the accumulation of nibbles can lead to exasperation, frustration, and burnout. In order to manage the nibbling, I have found a humorous way to highlight all those little bites out of my time, which has helped me cope with the interruptions as well as train my faculty to be more conscious of how often they come to me for help.

Dave Trott (blogger, 2024):

“Nibbled to death by ducks” is a phrase that’s decades old.

It refers to something being ruined not by a single powerful blow, but by a continuing series of minor objections and fault-finding until it’s unrecognisable.

I can't find many (any?) modern uses of 2. Pecked to death by a hen (except some by those living on farms and referring—usually jokingly—to actual chickens/hens).

A term that has been applied to this phenomenon is creeping normality. The relevant Wikipedia article explains:

Creeping normality (also called gradualism, or landscape amnesia) is a process by which a major change can be accepted as normal and acceptable if it happens gradually through small, often unnoticeable, increments of change. The change could otherwise be regarded as remarkable and objectionable if it took hold suddenly or in a short time span.

American scientist Jared Diamond used 'creeping normality' in his 2005 book Collapse: How Societies Choose to Fail or Succeed. Prior to releasing his book, Diamond explored this theory while attempting to explain why, in the course of long-term environmental degradation, Easter Island natives would, seemingly irrationally, chop down the last tree:

I suspect, though, that the disaster happened not with a bang but with a whimper. After all, there are those hundreds of abandoned statues to consider. The forest the islanders depended on for rollers and rope didn't simply disappear one day—it vanished slowly, over decades.

If you'd prefer a metaphor or a less prosaic fixed phrase, the article goes on to suggest quite a few, probably involving differing degrees of culpability shown by the 'venial sinners' [/'nibblers'], and certainly active vs passive involvement:

There are a number of metaphors related to and historical examples of creeping normality, including:

• Boiling frog
• Camel's nose
• "First they came ... "                      [Martin Niemöller]
• Habituation
• If You Give a Mouse a Cookie
• Lingchi – "Death by a Thousand Cuts"

...

• Normalization of antisemitism
• Normalisation of deviance
• Principiis obsta (et respice finem) – 'resist the beginnings (and consider the end)'
• Salami tactics
• Shifting baseline
• Slippery slope
• Technological change as a social process
• Tyranny of small decisions

If everyone takes just a little, a resource gets whittled away to nothing. Similar to erosion of a beach, cliff or shoreline.

To gradually reduce or erode something - emerged around 1746, shifting from literal wood carving to metaphorical reduction.

Similar words in same vein are "pare away" or "fritter away"

often mixed / paired with phrases like "to nothing," "at the edges," or "bit by bit", suggesting a slow, deliberate diminishing reduction.