If you strip the whole length of stranded wire and tin it first it will stay where you put it.
This does not make sense for CAT-5 applications.
It would involve stripping the whole length of CAT-5, unwrapping the foil, untwisting the four twisted pairs, fully stripping each of the 8 wires individually, tinning each wire, insulating the wires (in a way that preserves some kind of color code), twisting them in pairs, wrapping in foil and drain wire and insulating the whole package. That's a lot of work for a wire that is cheap and relatively easy to find in solid-core!