My theory is if the threads are cut, and you can see they are cut & seperating, then replace the tire.
I run Mr. Tuffy liners now and am not so worried about tire condition, but I still inspect regularly. As a commuter, I don't want to risk a tardy attendance on account of a shard of glass or a staple.
One time, I got a slice in a racing tire. I got a flat right through the liner and everything. I pulled out the offending object, patched the tube, and rode the last 80 miles of the century with the casing split & the liner plainly visible. There was a flap of tire coming loose near the end & I could feel it with every revolution, but the liner held everything together.
If you are concerned, Mr. Tuffy or the competing brand Stop Flat (No Flat?) is great piece of mind. Buying 1 size larger than the package says has been a good idea in my experience.