If you have a deferred payment agreement, it means you should not have to sell your home in your lifetime unless you decide you want to.
The money owed to the council from care home bills paid on your behalf during the deferred payment agreement will need to be repaid eventually. This can either be repaid by selling your house or you can arrange another way to pay if you are able to. For example, someone else could pay the money owed, or your family could use any pay-out from your life assurance after your death.
Your deferred payment agreement will end automatically following your death, and your executor will have 90 days to arrange payment of the money owed. If someone else (like a friend or relative) chooses to pay the bill, then your home will not have to be sold.