The photo below show what happened. I want to know how to reinsert that thing so that it stays put.
From the pic I can't really see the barrel of it, or the hole for the tuning post.
Those bushings (some people also call them ferrules or grommets) come in two basic kinds: one kind screws in - it's threaded on the outside - the other kind is a press fit, usually with little ribs around the diameter to help hold it in place. I think Epiphone uses press fit ones.
If it came out because the hole is worn, I'm not really sure that a permanent fix is practical in terms of the labor you'd have to put into it. I'd just put a little coat of glue around the outside diameter and push it into place.
If it came out because the bushing itself is damaged - maybe it got flattened a little bit somehow (although I can't imagine how that might happen). If that's the case, All Parts sells replacements: bushings and buttons
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