Later games in the AC series introduced the notion that the animus can play genetic memories encoded in DNA taken from any human remains, even remains that are many hundreds of years old. That DNA contains the encoded genetic memories of that person until their death. As long as you have access to sufficiently well-preserved DNA of the person you are interested in you can view their genetic memories from birth to death. Otherwise, you only have access to their genetic memories through the DNA of their direct descendants, in which case you can only view memories that were encoded from their birth until the conception of the child whose direct descendant's DNA the animus is reading.