A person stops living when they die. That’s clear. But that does not mean that the person does not stop being mentioned in records created after their death. It does not mean that people who knew that person instantly forget everything they know about them. It does not mean that their personal papers and effects instantly disappear.
Ask yourself what records might have been created after a person’s death that mention them? Their death certificate, obituary, probate/estate records, tombstone, etc. are fairly obvious. There are others: death certificates of surviving children may mention parents, obituaries of children may mention them, and so on.
Children, grandchildren, nieces, nephews, etc. may have memories of the person. The deceased person’s effects may be thrown out or destroyed or they may end up in the hands of family members.