I had one old tire delaminate on a Corvette. It was shaking the car so bad I couldn't read my gages and I replaced it before it let go. Turns out that was fortunate, as a few years later, I had an old tire fail on an Oldsmobile at 70mph. The tire steel belt broke and turned into a steel whip that chewed up the entire front of the car. $5k damage...inner and outer fenders, windshield, most of the side trim. The olds tire had no warning until a couple seconds before it destroyed the car.
So, the answer to how an old tire fails is by delamination of the plies. How and which plies separate is random, but the possible damage makes it worth getting rid of tires after 10+ years, unless you never drive on a freeway.
"The rest of the story": I had just purchased the Olds, and it did not come with a jack to change tires. I, rather lame brained, took it on a road trip from Ft Worth to Atlanta and back. It was on the way back, about 200 miles out of Atlanta, and on the part of I20 through Alabama that doesn't have exits but every 10 miles, and gas stations about every 3rd exit. This was 20 years ago, when I20 was not nearly as busy as today, and no cell phones like today. You could go for 10 minutes between seeing a car. As usual, I was speeding at 70 in a 60mph, and a gentleman in a Beemer was tailgating to keep from getting a ticket. The tire blew with an explosive "bang", with shrapnel flying all over. The windshield cracked from the blast as the steel tire belt beat the car to shreds. I pulled over...and the Beemer driver passed and pulled over about 100 feet ahead. I was excited, as I did not have a jack and I thought he stopped to help. Nope. He got out and walked around his own car to see if there was any damage...while I was walking to ask to borrow his jack. He finished the walk around as I got about halfway to his car...turned to me, flipped me off , jumped in and pealed out down the freeway.
I had to "limp on down the highway on the rim", to quote the song. "I reached a station down the road a ways", about 2 hours later, borrowed a jack, and finished the road trip at 50mph without further incident.