Sorry to revive an ancient thread, but the same thing just happened yesterday with a Trac Loader tire in front of my JD 4720 cabbie. This is not related to tractor make so I feel no shame posting it in the Kubota forum.
The issue appears to be related to intense cold conditions. I do commercial snow removal so the tires are usually kept at the minimal recommended pressure for 30-degree temps (12 to 15 psi in front) but I suspect the frigid air that hit us yesterday had caused the pressure to drop and the rubber to harden which is not good. I suspect the beads broke loose when I rounded a curve rather abruptly on a bumpy road. Did not notice it immediately because steering is jittery on rough surfaces anyway and I was concentrating on finding my way in severe drifting snow conditions. Only noticed it on the next hard turn. The tire had not popped out of the rim, was just hanging there. Front implement is a reversible snow pusher and it's quite heavy but there's a heavier 1-ton industrial blower in the back so front tires were not stressed beyond specs.
This is an old tire on its last season so I did not want to make a $300 service call and wait hours on the side of the road just to save an old tire and rim. So I slowly drove the 2 miles back home (tire popped out twice during the drive and I rubber-hammered it back in with some difficulty) and examined the damage. To my amazement there was surprisingly very little: none visible on the tire and a few barely noticeable dents on the rim. I guess driving below 10 mph has something to do with it. Once home I took the wheel off the tractor and stored it in the boiler room overnight where the temperature was about 90 degrees. This morning I removed the stem valve and pushed air into it at the compressor's max capacity. The tire inflated normally and re-beaded itself. Now I'm leaving it resting in the house until tomorrow to see if it leaks but so far so good. These tires are really sturdy, I guess that's why so many tractors come fitted with them when you order the industrial package.
Edit: apparently it is possible to inflate tires using the tractor's built-in compressor (for the seat) but I have no idea how it's done and could not find useful info about it online.