I haven't seen this answered yet so here goes...In Interstellar, what if Cooper never sent the coordinates to himself? When he's in the tesseract, he surely remembers receiving the coordinates of NASA. But suppose he never sends the coordinates...how would he get to the tesseract in the first place? At the moment of his decision, would he be instantly transported back to his home before the message (is never) sent?
The time travel logic of Interstellar follows the Novikov self-consistency principle (which physicist Kip Thorne, associated with the movie, did work on). Different time travel stories handle the logic of time travel in different ways. Consider the grandfather paradox, where you go back in time and kill your grandfather. In some stories, it's possible for you to kill you grandfather, but as soon as you do it you'll disappear. (I think in "Back to the Future Marty McFly starts to disappear when he makes changes to the lives of his parents.) In other stories, you can kill your grandfather, but then when you go back to the present no one will remember you, since you were never born. (That's similar to the plot of "It's a Wonderful Life.")
But my favorite kind of time travel stories, which include Lost and Interstellar, are the ones that don't have this kind of inconsistency, where it's impossible for you to time travel and do something that would logically make it so that you would have never gone back in time in the first place. Instead, you simply cannot go back in time and kill your grandfather: the very fact that you are alive means that one way or another, your grandfather is guaranteed to survive. So no matter what you try to do, you won't kill your grandfather, because the fact that you exist means that you didn't succeed in killing him. There is only one timeline, and all events, whether past, present or future have already taken place, whether you know about them or not. So you can only cause your past to happen (like save your grandfather's life), you can never change your past.
So the fact that Cooper received the coordinates implies that he DID send the coordinates. So the answer to your question "what if the coordinates were not sent" is simply "then he wouldn't receive the coordinates, and thus he would never have reached the tesseract." So Cooper didn't and couldn't have changed his past, he did cause his past to happen: it was his actions in the tesseract that caused him to go into the tesseract in the first place.
The Novikov self-consistency principle, by the way, is also crucial to understanding the movie as a whole. The aliens (revealed to be humans from the future) knew that Cooper's daughter Murphy was destined to save the human race. So they caused the past to happen: they set up a tesseract so that Cooper would go into it and convey the information (i.e. the quantum data) Murphy needed in order to save the human race. It's not that the human race originally perished but the humans from the future saved them; it's that the future humans brought about the events which they knew had already happened.
And also, this is more speculative but it's strongly implied that love is not just a product of evolutionary accident, but rather the future humans were the ones who were responsible for humans having love. And yet at the same time, the reason that the future humans are helping their past ancestors so much is out of love for their forbears. So they are giving their ancestors love, and they're doing it out of love! Novikov's self-consistency principle strikes again!
I thought a lot about this and becuase he already sent himself the coordinates (before he goes). I personally think him not sending the coordinates it would break the loop and return to the original loop which earth and everyone on it dies (but that's just my thoughts).
Late to the party but I hope my answer might be easier to digest compared to the answers above.
I personally believe in the many-worlds interpretation of reality. So given the possible scenario that Cooper might tried to be a jerk and not give the coordinates. It would simply open up another branch of reality where he exit the tesseract soon after and die in space because his daughter get into space and pick him up.
So think of it like this: Main Timeline 1. Mysterious branch open, cooper and gang travels to black hole and cooper gets into black hole. 2. Cooper is in tesseract, probability A: he gives coordinate, probability B: he doesn't give coordinate. 3A. Outcome A: Cooper goes back, save by daughter, rejoin main timeline 3B. Outcome B: Cooper goes back, not saved by anyone, died > Humans did not survive > hole is not created in reality B and Cooper didn't visit black hole so earth died.