canada common-law
This answer accepts the hypothetical and assumes nothing more in the contract than what is stated in the question. Therefore, it ignores the possibility of limitations clauses, liquidated damages, etc. This answer also ignore the effects of any statutory frameworks and is based purely in common law.
Expectation damages are the usual measure of damages for breach of contract — they aim to award value to the plaintiff based on the position the plaintiff would be in had the contract been performed (Bank of America Canada v. Mutual Trust Co., 2002 SCC 43, para. 25).
The rule of the common law is, that where a party sustains a loss by reason of a breach of contract, he is, so far as money can do it, to be placed in the same situation, with respect to damages, as if the contract had been performed.
Robinson v. Harman (1848), 1 Ex. 850, p. 855; 154 E.R. 363
Under Hadley v. Baxendale (1854), 146 E.R. 145, if the shipper B had special knowledge from which B ought to be able to deduce that there will be special loss to A should the delivery be late, then $10,000 would be included in the expectation damages:
if the special circumstances under which the contract was actually made were communicated by the plaintiffs to the defendants, and thus known to both parties, the damages resulting from the breach of such a contract, which they would reasonably contemplate, would be the amount of injury which would ordinarily follow from a breach of contract under these special circumstances so known and communicated. But, on the other hand, if these special circumstances were wholly unknown to the party breaking the contract, he, at the most, could only be supposed to have had in his contemplation the amount of injury which would arise generally, and in the great multitude of cases not affected by any special circumstances, from such a breach of contract.
Such a special circumstance arose in Cornwall Gravel Co. Ltd. v. Purolator Courier Ltd. (1978), 83 D.L.R. (3d) 267 (Ont. H. Ct.), affirmed on appeal in 115 D.L.R. (3d) 511 (Ont. C.A.), and affirmed by the Supreme Court of Canada in [1980] 2 S.C.R. 118. As summarized in M.J.B. Enterprises Ltd. v. Defence Construction (1951) Ltd., [1999] 1 S.C.R. 619:
Cornwall Gravel was awarded damages for breach of contract against Purolator owing to the late delivery of a tender prepared by the plaintiff. It was admitted that had the tender been delivered in time, Cornwall Gravel would have been awarded a contract for which it would have realized a profit of $70,000. ... since Purolator knew that it was delivering a tender which had to be delivered by a particular time, it “must have realized that if delivered late the tender would be worthless and a contract could well be lost” (emphasis added). The lost profits on the contract therefore fell within the rule laid out in Hadley v. Baxendale.
If that special knowledge isn't present, expectation damages is likely zero or close to zero.
Nominal damages, however, are always available for breach of contract, even if other measures of damage are zero (Atlantic Lottery Corp. Inc. v. Babstock, 2020 SCC 19, paras. 67 (Brown J., for the majority) and 105 (Karakatsanis J., dissenting, but not on this point)).
The circumstance you describe is almost certainly a material breach, so this would alternatively entitle A to rescission. Then, A could get restitution for what would otherwise be unjust enrichment ($10).
