In a number of occasions The Doctor explains "Fixed Points", moments in time which cannot and/or should not be changed, examples of these are the eruption of Mount Vesuvius (The Fires of Pompeii), the destruction of Bowie Base One (The Waters of Mars), and the 11th Doctor's death at Lake Silencio (Series 6)
We know what happens if someone tried to change a Fixed point,
Time fixes it up as it did when the 10th Doctor saved the crew at Bowie Base One, who were supposed to have all died, however the event is made public and Adelaide Brooke committed suicide to preserve the timeline
Time would collapse, unable to repair the fixed point on its own, as when River Song refused to kill the Doctor at Lake Silencio (eventually is fixed when the Doctor revealed to River Song his plan showing he was actually inside the Teselecta at the time)
However, I can think of 2 events which could have ended humanity which predate the events of Bowie Base One:
In Daleks in Manhattan, had the Daleks been successful we can probably assume that eventually humanity would have been wiped out or at least enslaved to be used to create new Dalek Hybrids.
In The Poison Sky, the Tenth Sontaran Battle Fleet planned to convert Earth into a cloning world. They released Sezerfine gas, poisonous to humans, so we can probably assume that had the Sontarans been successful humanity would have died.
These events predate Bowie Base One both in time they occurred and in humanity's technological advancement (the 2nd point, despite the existence of UNIT and Torchwood there wouldn't have been any planned/ongoing missions to set up a base on Mars).
I am wondering what would have happened to a fixed point in time if the past were altered so much that said fixed point couldn't possibly happen?