Not to belittle the O.P. or his question in any way, but I think this is a question better asked after week 2, or even week 3. I think we call all (or at least most) agree that the player in question getting cut before that would be a big surprise, and that means the the player will have another week or two of evaluation by the team. That's the usual approach with veteran players who've made it to the exhibition games portion of the off season.
There have obviously been exceptions, but I think a position as thin as run stuffing DT is likely safe from that.