You have no legal obligation for someone who is not your spouse. You can absolutely refuse to take any responsibility for his care. If he has no family, then the hospital will have to have county social services take over your finance's care.
If that happens, then you will be entirely out of the equation. I don't know what sort of financial issues this may raise, concerning your joint ownership or rental of property, etc. But, you can simply "walk away" from the situation, if you believe that is the best way to get your fiance' the necessary care he requires.
Note: I'm not making any moral judgment here. The law does not require that you accept responsibility for your fiance's care, so regardless of any emotional issues, you can simply refuse to get involved.
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