doctor who - If Amy Pond's parents were absorbed by the time rift, how is Amy alive?

We are shown several times over the course of Series 5 that the cracks do not operate like your classical paradox instigators. When they erase something from history, they do not create a new timeline with all of the new changes in place as one would expect (so for instance, it isn't like in "Turn Left" when a key moment in Donna's past was changed and a new timeline branched forth from that altered moment). What happens when the cracks erase something, on the other hand, is radically different. The erased object/person/etc. is taken out of history, as is everybody's memory of it/them, but their causal effects on the timeline remain. For example:

• When Amy's parents are erased, Amy remains in existence but cannot remember them.


• When the Weeping Angels on Alfava Metraxis were erased, the Byzantium still crashed.


• When a cleric on that same ship was erased, the communicator that he had given to Amy remained given to Amy.


• When Rory was erased, his ring remained on the TARDIS and his face remained in a photograph in Amy's house.


• When the events of "The Stolen Earth" were erased, their causal effects remained (the Daleks in the episode having come from the Medusa Cascade, the Doctor now traveling without Donna, the Doctor later regenerating during the events of "The End of Time", the meta-crisis hand Doctor which later became important in "The Time of the Doctor", etc.).


• Indeed, when the Doctor himself was erased in the finale, Amy's pictures and dolls of him, and the Earth itself which had been saved from numerous invasions by him by that point, were still in existence.

This aspect of the cracks' nature is consistently portrayed as such, and is indeed the reason why the Doctor is concerned - Amy reveals to him in "Victory of the Daleks" that she has no memory of the Daleks, which troubles him because there had recently been two very public Dalek invasions that she was unlikely to have missed, and going even further back, we learn in "The Big Bang" that the Doctor took note of how disproportionately large Amy's house for just herself and her aunt was and concluded that something must have happened since nothing else seemed immediately amiss. The entire point of this strange property of the cracks is very intentional, as the cracks are supposed to make the universe inconsistent by ripping up holes in it that don't make sense. That is what the Doctor comes to see as the very problem (e.g. "The girl who didn't make sense").

I, personally, compare it to ripping the threads out of a rug. If you rip out a few, you may see a gaping hole in the rug, but despite the threads on either side of the hole not being connected anymore, the rug itself still holds together. But the more you rip out, the more obvious the gaping inconsistencies in its structure become until finally, the whole thing just falls apart. However, for another perspective on the cracks which I feel illustrates their effects quite well, consider Lance Parkin and Lars Pearson's point of view, as they explains in the book: Ahistory, An Unauthorised History of the Doctor Who Universe (3rd Edition):

"However, do the Cracks in Time erase individuals from history entirely? Despite the Doctor's insistence about this, all the evidence says otherwise. When the Cracks 'erase someone from history', that person's absence does not create a new timeline - Amy not only keeps existing when the Cracks consume her parents, the alleged 'historical deletion' of her lifetime best friend and fiancé causes no long-term personality changes beyond her no longer being sad, as she can't remember that a Silurian shot him dead. Nor does Rory's 'erasure' seem to affect River - which it should, as he's her father. Granted, Amy is unique because she grew up with a Crack in her bedroom, but the same principle applies to four of Father Octavian's Clerics being 'erased'. If the Clerics 'never lived at all', then as each one is dematerialised, another should instantly appear. Octavian started the mission with twenty Clerics, so if four were retroactively 'never born', it shouldn't create a timeline where he only took sixteen instead. More noticeably, when the Doctor is 'erased', Earth in 2010 still exists. Considering how many times he saved the planet, deleting the Doctor from history should, almost without fail, result in a 2010 where Earth is under alien domination or totally destroyed. Similarly, Captain Jack's Torchwood team and Sarah Jane's adeptness at fighting aliens would never have happened without the Doctor, so every menace they defeated in their own series would be back on the table. What must actually happen when the Cracks consume someone is that said person's (to coin a term) 'temporal opacity' must get lowered to zero. The effects of their lives remain, but they're so 'temporally transparent' that nobody can acknowledge said effects. When Amy 'remembers' the Doctor back into existence, it's likely that her 'seeing' his existence and acknowledging him as real restores his temporal opacity to normal. This supports the continued (and otherwise nonsensical) claim that, 'If something can be remembered, it can be brought back...'"