How to fix a torn steel cable
You are looking at a swaged cable end, specifically a threaded tensioning type of end. Special tools are needed to perform the swaging, especially if the part is stainless. I've used hand swaging tools for aircraft cable, but the fittings are far more malleable than stainless.
But you're in luck, as my searches found swageless cable components specifically made for cable railings, or as in your case, cable fencing.
From the above linked site:

The one thing all of these Swageless Wire Rope Fittings have in common
is that there is no crimping. The swageless fittings that you’ll find
on this page are designed for cable railings. There’s two reasons for
that, one is that they’re Type 316 SS and the other is they’re
designed for normal working load limits needed to tension cable
railing. The push-lock and pull-lock designs are the fastest to
install because you insert the cable and it self-locks with the
internal springs. The other designs utilize a plug (sometimes called a
cone or wedge) which must be manually placed on to the center wire(s)
prior to securing the outer fitting housing. These swageless wire
fittings designed for wire rope fittings are field installed.

You may get away with using a joiner:

or any number of various terminators, including the quick attach stud version:

All images from the linked site.