DNA is "lego-like" structure from "lego"-blocks
ancient DNA is just a name of more or less long lego DNA sequence
let's say someone in the future finds a box of lego block but does not find any of lego-blocks built toys of our times
or finds sequences only of a few blocks
what would it mean?
another thing - lego blocks are made from a pretty sturdy material (actually like DNA). However, DNA is not the only molecule that can be a template for the protein assembly - RNA can do similar job. However, RNA is extremely fragile and degrades in minutes, and therefore cannot be found in fossils. Have you seen a cake made from lego blocks made from dough and cream? How long such cake will last?
If you don't find a dough lego, can you say that it never existed?
ps
i agree with these words from the first answer
"However, it's important to point out that the way this question is phrased makes it merely trivia, with no scientific significance."
"Cats have 90% of homologous genes with humans, 82% with dogs, 80% with cows, 79% with chimpanzees, 69% with rats and 67% with mice"
; so why not with an ancient ancestor of them we would not find the genetic similarity? $\endgroup$