The Epiphone Les Paul is a less expensive copy of the Gibson Les Paul electric guitar. It is mass produced to lower the cost. The jack socket is the part where the instrument cable is inserted. This part can come loose after some use. There are two different issues that can cause a loose jack socket. The method to tighten the jack socket varies based on why it is loose. The holes for the screws holding the jack plate can become too large for the screws over time, and the nut holding the jack socket to the plate can also become loose.
Shake the jack socket slightly. If the jack plate is moving, then the screws holding it in place are loose.
Remove all four screws holding the jack plate to the body of the Epiphone Les Paul. The jack plate and jack socket can be moved away from the guitar body.
Cover the body of the matchsticks in a little bit of wood glue.
Insert the bottom end of the matchstick into the screw hole. The head of the match should be sticking out of the guitar if it is still attached. Repeat this for all of the jack plate screw holes.
Wait for the wood glue to dry.
Break off any part of the matchstick that is above the surface of the guitar body.
Reattach the jack plate to the Epiphone Les Paul guitar with the screws. The matchsticks will provide extra material for the screws to grip to in the guitar body. This will tighten the jack plate in place on the guitar.
Shake the jack socket slightly. If the jack plate is held securely but the jack socket is loose, then the nut holding the jack socket down is the issue.
Unscrew all four screws that hold the jack plate to the Epiphone Les Paul to remove the jack plate.
Lightly grip the back of the jack socket behind the plate that is now exposed.
Turn the nut on top of the jack plate clockwise. This will tighten the jack socket. You can tighten this nut by hand. You do not need to use tools.
Replace the jack plate. Screw all four plate screws back into place.
The jack socket is wired to other electronics in the Epiphone Les Paul electric guitar. A loose jack socket has nothing to do with the electronics. The length of extra wire can vary between guitars. Do not pull the jack socket or you may break the solder connections that hold the wires in place.