In Looper, at the end of the movie young Joe shoots/kills himself and old Joe immediately ceases to exist anymore. Earlier in the movie young Seth lets his older self get away. Once YS is caught his bosses start amputating parts of his body (which OS also immediately loses) in order to get OS to turn himself in. Why didn't they just shoot YS so that OS would just vanish?

Why even have Loopers at all? Each Looper is established as having his own designated execution spot, which doesn’t have any specific preparation except for putting a little plastic tarp down. So if the future evil crime time travel machines can drop their victims anywhere on Earth… why not program them to drop their victims at the bottom of the ocean, into a volcano, or some other extremely secretive and hard to find inescapable death trap? Apparently, the super evil crime lords of the future picked a complete idiot to run their Looper program, since Abe decided the best way to dispose of people was to have idiot junkies kill them alone out in the middle of nowhere without any way to definitely guarantee that the victim has been actually killed.

From the writer: “People in the future, all they know about time travel is to be afraid of it. So they’re trying to keep it as tight as possible. So the initial reason they set it up this way was to keep the causality loop as tight as possible,” Johnson said. Because, for example, if someone else kills your older self and you have to exist with your own murderer for 30 years, what’s stopping you for murdering them or doing something to screw everything else up? ”Every bit of evidence is gone from that loop when you kill yourself,” he said.