I need advice around a sticky family situation but don't want to talk sensitive details with people I know in real life. Please help?

I have an aunt and uncle who have chronic financial problems, stemming from a variety of serious health issues (both physical and mental). Due to a series of unfortunate external circumstances, their financial problems have escalated recently, and they're in danger of being evicted from their house (among other things).

I'm a young university graduate with a stable, modest income. I make enough money to cover my payments, and save a bit for the future (I'm anticipating grad school and possibly children in the next 5-8 years). In many ways I am much, much more privileged than they are. I really want to offer them some money, but don't know if I should, for a variety of reasons.

So, I put it to you lovely people: would I be stupid to offer them financial support? (It would be hard to be a one-time gift—their need is constant, with no real end in sight.) Is there any possible way to make such an offer without deeply offending them and hurting their pride? I know they find it very painful to accept money from anyone, and I'm still seen as one of the "kids" in the family.

My parents and grandparents have stretched themselves thin over the years trying to support them, but are unable to sustain it much longer. I'm really worried for my aunt and uncle, and especially for my cousin who's really had a rough go of it. It's a shitty situation, and I don't know what to do. :(

ETA: Wow, thank you all so much for the amazing kindness and support. I really appreciate everyone's empathetic, level-headed advice. Thank you all <3