We electricians have many tricks, but there’s one thing we can’t do: stretch a wire that’s been cut in the wrong place. Instead, we splice it.
For a wire that’s cut too short
A wire that’s cut too short in a box is an Electrical Code violation if it’s connected as is to a receptacle or switch. It’s usually fixed with a pigtail splice—a longer wire joined to the shorter. Many people use twist-on connectors (a.k.a. Marr connectors, after a common brand), but they can occupy so much space in the box that the receptacle or switch won’t fit. Push-on connectors are a newer, simpler splicing solution. They’re sized to fit various wire gauges, and some have multiple ports (you can splice three or more wires together). A pack of 10 at any hardware store should run less than $5. They cost more than regular twist connectors, but they’re almost foolproof to use: just strip the end of the wire and push it into the connector.
For a buried cable that’s been severed
A cable that’s been buried by a shovel gets me called out to many cottages. Rather than dig up and replace the cable, I often use an underground cable splice kit—a four-position barrel connector and a sleeve of thick heat-shrink wrap. Connect the wires, slide the sleeve over the connector, and heat the sleeve to shrink it to a weatherproof and code-compliant seal.