Soldering a broken Rx antenna OK?

[Finnster]

I thought it was a coax too, but after I inspected it it didn't seem so.

It has a grey outer coating, and a silver sheathing below that, but the core is a single multi-strand wire. Perhaps the silver sheathing is part of the coax, but it doesn't seem insulated from the wire core, so IDK. The wire is so thin its a bit hard to tell. It doesn't seem like a cable coax where there is insulation-sheathing-wire-plastic core-core wire (going from out to in.)

What would be the purpose of a coax anyway? The antenna is not actually connecting something. not sayingit isn't it, just can't see it. hmmm....