A recent answer included this:
Actually rocks in tire treads can be life threatening, if they gradually cut through the rubber and eventually cause a blow-out, and you don't usually get any warning about rocks in tire treads, unless you look for them regularly. Source
The last sentence about not getting any warning is false, a rock in a tire tread sounds like winter tire, but with only one stud in it. I suppose if you have the music really loud, or no exhaust, or something there could be a scenario where you didn't hear for a long time. But usually you know there are there, in my experience they have normally cleared themselves in a 100 miles or so.
I Googled and found a couple of pages about common flat issues and a rock in the tread is not mentioned.
Could a rock stay lodged in the tread, for a really long time and cause a blowout?