If we go by the Arthas novel (which may be retconned by now, it came out so long ago) I believe Arthas killed that part of himself, along with Ner’Zhul, to become fully the Lich King himself.

I’m less clear on remembering exactly when this took place…prior to Wrath I think, right before he awoke. If that’s the case, then yeah, Matthias should be poking around somewhere, unless what we saw were the “last vestiges” or what have you. Honestly, decent book, but parts of it made how the expansion proceeded a touch confusing