A common way to cut a strop is to flip the blade before you reverse stropping direction. While it is pretty obvious that this should never be done, sometimes the motions get really fluid and bleed together

Another way that I have nicked a strop (much more common on knives than razors) is when I set the blade on the strop, and before I intend to start moving, the blade moves in any direction other than spine leading as I find my angle. A really soft strop and a really sharp blade...cuts can happen almost without realizing it. Most commonly the blade moves in a direction nearly parallel with the edge (just like when you cut your face shaving...that (in theory) should never happen either)

In the end, its like locking the keys in your car...it SHOULD never happen, but when you let your concentration lapse, or try and get in too big of a hurry and stuff happens