As her husband he is legally responsible for her support. If he is not paying for her support, someone, as in you, can go to court and get guardianship/conservatorship over her and then that person can require that her portion of the house be removed from the trust. In a living trust the person who owned the asset still has control over the asset and I assume that the house is in both of their names. He has probably named himself trustee but I question how he could transfer the house to the trust if she is not competent.
You would file at your local probate court and most have a self help page with instructions and forms. In most states, you will need two doctors to examine her and certify that she requires a guardian.
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I imagine the problem with Medicaid (I don't think it is Medicare) is that the transfer was made within the five year "lookback" period. Once you are past the five years, then she should be eligible. However, this does not change the fact that as the spouse he is responsible for her care. Someone would really need to look at the trust document and see exactly what transpired. Based on his actions, I still recommend getting a guardianship.
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