Things You'll Need
Electrical box cover
Spray foam insulation
Drywall joint compound
If you can't pull the old wire out of the wall, disconnect it from the switch, then snip both ends of the cable so there are no exposed wires and wrap them with electrical tape.
As long as the cable remains connected to the switch, the other end has to be placed inside a covered electrical box, and the ends of the wires must be capped.
Putting up a wall lamp is not a difficult task, and taking one down is even easier. When the lamp is gone, though, you'll have a hole to patch if you don't plan on replacing the lamp with another one. There are two strategies you can follow, depending on your long-term plans. If you are sure you will never install another lamp at that location, it's a good idea to disconnect the wires. If you would like to leave the option open, just cap the wires inside a covered electrical box.
Turn on the light switch, then flip off breakers in the main panel until the light goes off. Leave this breaker off.
Unscrew the light fixture from the mounting plate attached to the electrical box. Pull the fixture off the wall, then unscrew the wire caps connecting the light and circuit wires, untwist them and remove the light. Unscrew the mounting plate from the electrical box.
Twist wire caps on the ends of the black and white wires and push them into the electrical box if you want to install a new light at that location in the future. Screw a cover onto the electrical box. Electrical box covers are readily available at any hardware store. You may want to paint the cover to blend with the wall, or hang a picture over it to hide it.
Unscrew the wire clamp holding the cable to the electrical box and pull the cable into the attic or basement if you want to keep the cable accessible for a future installation. Nail a junction box to a stud or rafter, feed the cable into the box and screw on a cover.
Disconnect the wires at the switch if you plan on permanently removing the light. Turn the breaker back on, then test the leads on both switch terminals with a voltage tester. The live circuit wire will light up the tester. When you have distinguished the wires, turn off the breaker and remove the other wire from the terminal. Untwist the white wires, then recap the white wire from the live circuit. In the same way, untwist the ground wires, but leave the ground wire to the live circuit connected to the switch.
Pull the cable that went to the light into the attic or basement and remove it. If the fixture was mounted on a remodeling electrical box, unscrew and remove it. If the electrical box is nailed to a stud, you can leave it in place.
Stuff some newspaper into the hole. If there is still an electrical box there, fill it about half full. Spray some spray foam insulation into the hole, and let it expand to fill it. When it dries, cut it flush to the wall with a utility knife.
Spread two or more coats of drywall joint compound over the hole with a drywall blade to patch it and blend the repair into the wall.
Chris Deziel is a contractor, builder and general fix-it pro who has been active in the construction trades for 40 years. He has degrees in science and humanities and years of teaching experience. An avid craftsman and musician, Deziel began writing on home improvement topics in 2010. He worked as an expert consultant with eHow Now and Pro Referral -- a Home Depot site. A DIYer by nature, Deziel regularly shares tips and tricks for a better home and garden at Hunker.com.