If you're trying to support your subjects with money, use Give Subsidies. Jack the amount of time up as high as possible (you can always cancel it) and give them whatever you want. Subsidies seem to work better than lump sums (gifts or loans even if you could do them) because they impact the subject's income, and higher income will open more options for budgeting for them. Of course, if you do have intentions of dropping it, be careful because you could get them to buy armies just to delete them again.What's worse, they don't accept loans no matter what. I have this huge pile of cash I am willing to dole out to my subjects in case they need it, but no, they'll refuse loans even if their debt is so huge it will take them decades of trying to get back on their feet. They just don't accept them and all I can do is grant that cash to them for free.
I have never seen AI accept loans from me, ever, vassal or not.