> if you fall in a coma for a year, you might wake up homeless
No, you would wake up, as scythe has already pointed out, with a tax lien on your property--which you could of course remove by paying the taxes owed.
If you own your home, you can't be evicted from it the way a renter can. The only way to force you out of your home would be to take away your title to it. I'm not aware of any jurisdictions where this is actually done for non-payment of taxes, though.
A much better case can be made that you don't fully own your home if you have a mortgage on it, since the lender has the right to foreclose, which means they take title to the property, if you don't make your mortgage payments for some period of time. (Ironically, your property taxes if you have a mortgage are being paid out of an escrow account, so your mortgage lender will see the consequences of non-payment well before your municipality will.)
It takes years to decades for a tax situation to reach the level of fourclosure on reasons of property tax and if a reasonable issue for health or otherwise the state could even waive it due to non-use.
I'm sure every state is different, but there are places where the state can enforce their tax lein by foreclosing and taking ownership of your property.
A lot of the time this is simply handled by placing a lien on the property due at sale or transfer. Your kids might not be able to inherit it, but inheritance is another question altogether.