Here is one that was caught by my TPMS. It is a 3/8 by 2 inch bolt that was picked up on the highway.
My TPMS was showing one of my trailer tires down a couple psi from the others. I pulled over at the next truck stop and noticed it was down a little more. (I routinely check tire pressures as I drive. Helps reduce the monotony of driving).
Looking at the tire I found the bolt. The pressure was still above the alarm point. I had to go around some garbage on the road about 100 miles before this. It appeared to be a battery carrier. This 3/8 x 2 inch bolt must have been on the road in the left lane where I went to miss the rest of the garbage.
This is a case where pressure checks and walk around would not have saved me from a tire failure.
The TPMS saved me problems and gave me time to find a level shady place to put my spare on. (Southern Arizona in 95 degree weather with full sun)
And it is possible a TPMS would have alarmed for the OP before the tire failed from the nail.