It is interesting to consider what things change instantly in the future when things change in the past; but it is even more interesting to contrast these against what things do not change instantly in the future.
The easiest way to illustrate this is probably to consider Seth. When Old Seth runs, Young Seth is grabbed by Abe, and then two things happen to Young Seth, probably simultaneously, one of which also happens to Old Seth, but apparently not the other.
One thing that happens to Young Seth is that Abe’s surgeon carves a message in Young Seth’s arm; it immediately produces a wound which will scar. It is obvious that this also happens to Old Seth, because Old Seth then sees the scar.
The other thing that happens at that same instant is that Young Seth decides that running is a very bad idea. We can be quite certain that even if Abe were to stop at this point, Young Seth would never run; he recognizes the folly of such an act. Yet this does not happen to Old Seth. We know that it does not because he continues, for the moment, trying to scale the fence into the rail yard, until he realizes that his fingers are vanishing.
Thus physical damage to a person is instantly part of the body of the person in the future, but psychological damage is not part of the person’s mind.
The film is consistent in this, and it is a necessary rule for the ending to work. After all, Old Joe is set on killing Cid. As he pursues his objective, Young Joe shifts from trying to kill Old Joe so as to save himself to trying to protect Sara and Cid, because he cares about them and believes that Sara might be able to raise Cid to use his power wisely and well. Should Young Joe live, it is likely that he will never meet the mystery woman who saves him and becomes his wife; Sara has already saved him, whether or not she survives, and he has no chance of living that other life or ever developing that relationship to that woman. Sure, in a sense it has not yet “unhappened”; but at this point Sara and Cid matter to Young Joe in a way that says they should also now matter to Old Joe.
So again the film disappoints with its inconsistencies: physical change moves through history in a way that does not make sense, but psychological change fails to move through history in the same way even though that would make more sense. It is as if a looper’s older body is connected to his younger body, but his older mind is not really connected to his younger mind, that he never was that person and the changes to that person don’t affect him, only the changes to that body.