Paying for care fees in wales

Hi, I am trying to understand the care system in Wales. My mum will need home care or possibly residential care. My dad wants to move and my siblings have talked about possibly selling up and renting to live closer to the village which I think is a bad idea as if you have move than 50k in the bank you have to pay for all care fees.
I have spoke to Age Cymru but am still a bit confused. Say if my mum is put into a care home and my dad is still living at home and he passes away could the local authority sell the house and then back pay all my mums previous fees and use the rest to pay her future care fees ? I just want the best for by mum n dad and don’t want then to unnecessary pay for care fees if they don’t have to. Appreciate any help !