What you are asking about isn't going to be answered adequately on a public forum. Hire a local lawyer with a lot of experience in this stuff is the best advice you are going to get.
Tough situation, hope it works out. Honestly though I would start preparing for answers you don't want to hear.
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In broad strokes I can tell you that generally Medicare doesn't pay for long term care. It will pay for a short stay in a facility for rehab purposes. Beyond that you are depending on Medicaid.....which is for people who are already broke. How broke is "broke" depends on state law. It's not like you're the first family to think about making sure mom doesn't have any assets _after_ she gets sick, and mostly the regs are going to prevent you from doing that and then relying on aid meant for people who don't have money. The details vary from state to state, and as I said you need a local estate planning attorney that knows the ins and outs.