It's sort of how you handle assisted living costs. Everything's cheaper if you've distributed your assets beforehand.
Every rich person has a guy who will tell them how to avoid it legally. Every poor person never had any money in the first place. It only ever hits middle class and upper-low class people who saved money for some of their life and were never told that they had to disburse their assets at X-1 years before they planned to need care and get hit with a huge penalty to their assistance when they inevitably have to move some of their cash around to pay for some of their expensive care.
If you don't want rich people getting public funds for things, you have to be able to look beyond their money games, which is hard, expensive, often purposely sandbagged, and not usually successful.
So just tax them their whole life instead, and let them get back some of what they put in with every other person.
I am relatively poor and this will help me because even though I am poor I still have to prove I am poor which is burdensome.