Can the well spouse sell a rental property owned by the one in memory care?

To be honest, not sure how they could have sold without proof of ownership or a POA. The realtor has to see a deed and a POA has to show he is allowed to sell. It will be in the POA papers. So, there was a way the person got around this. Memory care cost a lot. Maybe the money is being used to pay for that.

How are the affected spouse's finances currently managed, then? Bills paid, bank accounts tended, that sort of thing?

If the rental property needs to be sold to pay for the memory care that would certainly be a legitimate use of the asset; but I agree with Barb that you'd best get legal advice on how to go about it.

This question really needs to be asked of a lawyer. But bumping it up.