What's the name of this connector?
Looks a little like a bullet connector / terminal.



If you have access to the other end of the connector that you think is broken, you could disconnect it &amp; test the wire to see if it's really broken using a multimeter (set to ohms / resistance), or test it in place with the power off. Maybe that wire's not the problem, there are a lot of other electronics in there too.

Most light fixtures just use cheap wire nuts to twist two wires together, you could just cut &amp; strip both ends of the wire and use a wire nut.

PS Don't forget to check why it was pinched &amp; don't do it again.