I had to grapple someone with a shoulder injury recently.
At Fabio's, like most places I am sure,we are not wise enough to take time off when we hurt our selves. We stupidly power through the pain risking further injury because, you know, taking a week off to heal up is just a poor use of time. lol So, people with shoulder or elbow injuries often tuck the offending arm in the belts and grapple one handed.
You'd think grappling someone with one less arm would be advantageous... but it isn't. At least not when it is the arm on your go to side. I had nothing to get a hold of, and no arm to tuck neatly at my side when in side control. ..which left me very little control.
It is good practice though. It makes you think outside the box.
Fabio actually has us do that sometimes on purpose. One person will have to tuck both their hands in their belt.... the result is generally a cruddy grapple, but a cruddy grapple in which you learn you can do amazing things with your legs if you have to rely only on them. Either way though, I don't like to be the one with two arms grappling the no armed, or one armed man. I like having handles.