There are many instances, particularly in Parts 2 and 3, where Doc or Marty travel to the past to accomplish some goal, but when they succeed in that goal, they eliminate the original purpose of going back. (Going to 1955 to retrieve the almanac, saving Doc from the west and destroying the tombstone, the list goes on.) This would seemingly be a variation of the Grandfather Paradox, as we are led to believe that BTTF exists on one constantly evolving timeline. But even though there is only one timeline, we have several different "realities" or "versions" of that timeline. (1985a, Twin Pines 1985, future where Marty gets in an accident)
The problem is that once one of these alternate realities get erased, people in
that reality aren't supposed to affect the timeline anymore. Take 2015 where Biff steals the almanac. If Old Biff from 2015 goes to 1955, only to create an alternate reality where Doc and Marty don't show up in 2015, how can he go back in time with the almanac? The answer, I think, is that no matter how many times you alter the timeline, an "echo" of older versions of time travelers must still exist to complete whatever action they are meant to complete.
To illustrate this more clearly, let's look at Part 2 when Doc and Marty go back to 1955. They see Old Biff hand over the almanac, an almanac from a version of 2015 that no longer exists. The Old Biff they see can't possibly be who Biff grows into anymore either, because once he gives Young Biff the almanac he creates 1985a. Doc and Marty would have had to take the time machine to 2015a in order for that Old Biff to even have a chance of using it. Therefore, this Old Biff should not exist. BUT HE DOES...He exists as an echo, a remnant from a destroyed reality. As soon as Old Biff drives off from 1955 at 88 mph, he'll just cease to exist because there's no timeline for him to go back to.
There are several "echos" present in the series. Once Marty goes back home in Part 3, the version of him in 1955 who travels to the Wild West must also be an echo. In BTTF the Game, there is a Citizen Brown timeline where the time machine was never invented, yet we still see Doc and Marty in a photo taken in the 30s. They were echoes.
Any thoughts on this theory?