There are 'living fossils" such as the coelacath that have been unchanged for long periods of time. It's due to they being adapted to their environment and the environment not changing.
The 'Bigfoot" existence is unlikely. Ten million years ago there was a giant ape, Gigantopithecus that would seem to meet the requirements for a "Bigfoot" ancestor.. However, the ape lived in SW China and died out some 300,000 years ago.
To be "Bigfoot" the ape would have had to migrant to the Americas and survive. That's not likely.
The major problem with "Bigfoot" is having a viable population. The brown bear lives in much similar environments and eats many of the same things "Bigfoot" would. There's some 700,000 brown bears in North America. They are so plentiful that hunting is allowed.
The problem with "Bigfoot" is that to have a viable population, we'd have many more encounters. Last summer we took a bus trip and saw 3 bear inside of an hour. Bear get hunted and shot, bear get trapped, bear get hit by cars. However, not "Bigfoot."
Certainly it's possible that Gigantopithecus made it to the Americas, survived and evolved into "Bigfoot." However, we don't have the bodies. A viable population, or even a shrinking one would still provided specimens. However the last "Real Bigfoot body" turned out to be a rubber suit in a freezer.