I happen to be Jewish, so my answer might not match that of the Catholic theologian.
Yes, Terri has a soul, which is no less valid than the soul of a perfectly functional human being. This is what makes her starvation and dehydration dictated by a presumably secular judge so abhorrent.
You win a cigar for a perfect answer. A Catholic Theologian would have to give the same answer.
What they are doing is killing a soul.