When someone dies and one of the owners dies the house will still remain in the living owners name and so they will continue to own the home.
For example if a house is in both the wife and husbands name and the wife dies then the husband will retain ownership of the home.
Or if the house has been put in both the parents and at least one of the kids names then the house would transfer ownership to the kids.
If you have a mortgage and the mortgage for the house is in both spouses names then the living spouse would be able to continue to make the mortgage payments if they have the money.
If they cannot pay the mortgage then the mortgage company or bank will take the home.
But if the house is owned outright with no mortgage then the living owner gets to keep the house and it's a good idea to have the house in a family members name such as an adult kids name should both the parents die.
If the house is paid off then the kid would get the house and can then either sell the home or live in the home themselves.