What is this connector type and how to connect to a loose wire
Its a wire ferrule. It's crimped on and provides a better connection in screw terminals than bare stranded wire. It provides a solid profile vs stranded wire so less likely they will shift and loosen and pull out or for heat cycling to be as problematic. Also makes less likely a rogue strand will short out to something else because its all inside the ferrule body.
https://en.m.wikipedia.org/wiki/Electric_wire_ferrule
If you are trying to join it to another wire, you may be able to solder to it or just cut it off. You may be better off using an appropriate in-between connector like a screw block or terminal block or wago connector.