What happens if the grant requirement for open access publications is not respected? [small & short-duration grants]
I'm most familiar with the US NIH.
They write:

Non-compliance will be addressed administratively, and may delay or prevent awarding of funds.

For the most part, NIH seems focused on awareness and trying to encourage compliance, rather than strict enforcement. It seems many are not fully aware of the guidelines, which are quite new for some researchers who have published a different way for decades.
More generally, big funding agencies like to act through the institutions researchers belong to in encouraging compliance, whether for policies like this or for ethical policies like those for human/animal subjects research.
They can threaten to withhold their funds and even government funding more broadly from entire institutions, not just individuals. While cases of this threat actually being carried out are rare, it may mean that researchers find themselves more directly responsible to their institution rather than the funder. The institution has a large incentive to ensure local compliance and likely has more resources than the funding agency to follow up, as well as a broader range of sanctions.
For your particular situation, I have a hard time imagining a funding agency feeling too bad for your circumstance. If they're funding your work and demanding open access, they're implying that they expect you to use their funds towards those costs in addition to all the others (either directly or through the fungibility of money). &quot;I spent my money on other things and now can't afford to comply with your publishing requirements&quot; doesn't seem like a very good argument, since everyone they fund is in the same boat and since you've accepted their terms by accepting their funding.