Hi John! It’s an interesting question… it really depends.
Sometimes we don’t know that someone has passed away — in those cases, nothing happens. Many postcrossers will slowly stop their activities on the site as their health declines, and after some time, their accounts are switched to inactive automatically.
Sometimes, a friend or the family will reach out to us. If it’s a friend, we’ll try to verify the information so that we can register the postcards and lock the account until someone logs in again or contacts us.
If it’s the family, we offer to register the incoming postcards so that they don’t have to worry about it in the middle of their grieving. After that, what happens is up to them: some people want to keep the account as a sort of memorial to their loved one (or to let the community know), others would it like it be closed, and others still will continue the hobby further.
I hope this helps!