Chaos theory tells us that, despite how orderly a system may be, there will always be slight variations with every repetition. Steps can be taken to limit the magnitude of the little incidents and cancel out most major incidents entirely so that the system continues to function as planned, but not every possibility can be predicted. Eventually, something will fuck up big-time and wreck everything. With that in mind, there are basically 2 timelines shown in the movie - A, the “main” timeline and B, the aberrant one. Timeline B is actually the bulk of the entire movie, from start to finish. Timeline A is only shown in the flash-forward bit and isn’t actually just one timeline - it’s representative of countless others.
When I was a kid, there was an old Hot Wheels track you could customize with all kinds of twists, turns, loops, etc. and your car was launched through it via those little spinning wheel accelerators. It wasn’t one-way, though. The track pieces were designed to be a closed circuit, where you’d be launched through all kinds of shit, but ultimately loop back around to be shot through it again. This is the thousands of histories that I refer to, collectively, as Timeline A. Joe grows up, becomes a Looper, lives off of his golden payday for 30 years and is eventually sent back to be killed by himself & kick things off all over again.
As it says in the movie, time travel is messy, so Joe doesn’t always have the exact same life, he just has the same beginning & end. Maybe in some variants of Timeline A, he goes to France instead of China. Maybe in some, he doesn’t marry his Chinese wife, or stays addicted to the eyedrop drug. Maybe…you get the point. But he always comes back and gets shot by himself. Listen when he explains what “closing your loop” is, how it doesn’t attract the most forward-thinking bunch and so on. While his stashing a fortune in silver is evidence of him intending to fight his own loop being closed by disappearing, he’s ultimately at peace with the possibility and, for the most part, it happens every time. No matter what he does, for countless iterations, Joe is caught after 30 years and sent back for closure. But then…his wife is shot. And this changes everything.
This one event, obviously, has never happened in any of the Timeline A’s. You can tell because, for the first time, Joe isn’t just resigned to his fate - he kills the Rainmaker’s agents and goes back to kill Cid in order to save his wife from being shot, thus creating Timeline B. Because he created an aberrant timeline, all the rules go out the window. There is no set future yet because, from the moment Old Joe fights his loop being closed, Joe, Kid Blue, Abe, Cid, Sara & everyone else are trailblazers in a new timeline. However, while time travel is messy, it doesn’t mean that loops won’t or can’t be closed - Joe proves this when he offs himself to save Sara. It just means it will have to be closed a different way from how it happens in Timeline A.
You can see evidence of what I’m talking about in the way Old Seth & Young Seth die. An online review brought up the point that, if Seth has his limbs cut off in the past, his older version should’ve come back without them from the get-go and not just started losing them when Young Seth got captured. Wrong - the Old Seth that comes back is from Seth’s Timeline A, but something happened this time that caused him to start singing & create a Timeline B when Young Seth allowed him to run. From that moment on, while the two Seths are still linked by causality (resulting in the most brilliantly, godawful horrifying use of time travel physics I’ve ever seen) their future is unwritten, so Old Seth kept his limbs up until Young Seth got carved up because Old Seth originated in Timeline A and could only be affected by events in Timeline B as they occurred, since they never for him before.