There should be a little tab on the side of that lock cylinder, at the inner end, that has a spring under it to push it out a little. That is what holds the cylinder in to the handle. Either that is damaged, or stuck in, or what it hooks into inside is broke. Look for that little tab and see if it can be pushed in and pops back out. If it's stuck, lube it. You'll have to push it in, then insert the cylinder back in the door in the correct position and see if it stays in.
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