Never broken a chain in all my 60odd years of riding.
However, a few years ago, the KMC Missing link went "missing" as I was descending a very long hill. The chain fell off at some point, but I never noticed for ages until I started climbing the next hill. I was only three miles from home, some of it downhill so I did a mixture of walking and freewheeling back.
In the three miles home, I didn't see my missing chain. It took another ride later in the day (with a spare chain fitted!) retracing my steps before I found it.
Maybe it would be easier to take a spare chain than try to fix one.

Mick F. Cornwall