The main problem would be one of scale. As a general rule, and ignoring things like defaults for a second, it takes the same amount of effort to service a small loan as it does a big one - same systems, same people etc. Obviously there's economies of scale, but even if you run such services at cost, those costs are high.

And because the initial loan would be so small, the amount of 'fair' interest on it would be tiny. It simply wouldn't cover itself.

Then you add in what would be undoubtedly a higher than average instance of defaulting, the costs go up even more.

Then you factor in the realities of any kind of emergency lending - that people typically borrow without the means to pay it back without borrowing again - and you're still creating problems at any amount.

There are better ways to deal with the problem, handing out money in any amount is usually not the answer, and especially not if it needs to be repaid, with an amount of interest that covers the costs of delivering the service, even if it's a non-profit.

Also worth mentioning that I've seen many 'hardship funds' over the years, from local businesses who will actually hand out small cash amounts for people who need it. I don't know if they're still a thing, or were a consequence of the last decade when 'being charitable' was a high-vis way to gain popularity.