Yes, it is absolutely possible to fire an 8mm in an '06. No, I have never done it, but I have seen the fire-formed brass personally, and have also read about it in old gun magazines.
I sure as heck wouldn't do it on purpose, but I imagine that the round would headspace on the bullet after pushing it back in the case, then fireform the case to the '06 chamber. The lower pressure from the lighter loading and the larger chamber, I would think, would be offset by the higher pressure from the force needed to swage a .015" larger diameter projectile down the bore. Apparantly the pressure is not too great, because this is the fifth or sixth time I've heard about this happening, and I've never heard of a rifle blown up from it.
Now, as others have said, take a full-load military or European 8mm round, especially with a thick FMJ or steel core bullet, and I would expect the results to be quite different.
On a related note, someone once gave me a bunch of brass they had collected. There were a few ".303 Savage" empties mixed in. As any old-timer or cartridge collector knows, the .303 Savage was a lever-action round from way back, very similar to the .30-30 Winchester. These, however, looked very odd, being blown out (fire-formed) and bulged real bad. I went and got a fired .303 British and compared the two- sure enough!
"Well, dang, JimBob, these here three-oh-three boolits jist ain't workin' right in my ole three-oh-three. I caint hit nuthin, and they aint workin' right in the clip"