I do this occasionally when stuck for a quick connection.
I use stranded or solid wire who's jacket diameter just fits within the inside of the coax plug. Standard jacketed 2 conductor stranded #22 wire fits nicely inside a 2.1mm jack - either shielded or unshielded cable. Cut off the shield if there is one.
Identify the conductor that you want to connect to the outside barrel. Strip about 1.5" - 2" of the conductor insulation and wind the bare conductor tightly around the barrel. You want at least 2 or 3 full turns. Then twist the wire really tightly against itself so as to make a good, solid connection.
You do the outside barrel connection first so that you can twist it easily and get it tight.
Now measure the remaining conductor so that it is about 1/4" longer than the depth of the inside connection. Strip about 3/16" of the jacket, fold it flat against the plastic conductor insulation, then shove it inside the barrel plug. This should be a very tight fit. The bare conductor makes a good connection with the inside of the barrel plug and the conductor insulation provides a compliant pressure to keep the conductor tight.
This is a semi-permanent connection that will last for months or years so long as it is not disturbed. Nonetheless, you really do want to replace it with a proper connector as soon as is practical.
The advantage of this technique is that it doesn't damage the plug. The wires are easily removed when needed.
I'll post photos when I figure out how to do that.