The Kevlar/Spectra/Dyneema cores will not melt like the poly sheath, or solid nylon.
Melt the sheath, and using a folded paper towel, wipe the HOT! sheath over the end to enclose the core. (Pull the line through the towel or the towel over the line, don't "dab".)
Edited to add: Sometimes I pull the sheath down a bit, cut off the core, slide the sheath up, then melt down to the core. Be sure you melt a bit of the core and capture it in the sheath bead.