I have worn a boxing glove Art Jimmerson style to class for 2 months due to thumb injury.

Also have trained with one wrestling shoe due to big toe injury.

That was in regards to how to get me back to the mats ASAP. Usually when I've been forced off the practice completely I've tried to get my other aspects of life in order, maybe do conditioning but not focus on BJJ too much until I can at least get back to the mats easy.

I've been lucky so far in that all of my injuries in BJJ haven't been so severe that they've completely kept me off the mats for more than a week. Worst was probably hurting my back and fucking up a kettlebell swing with one that was too heavy for my technical level back then. I couldn't train during my BJJ class the next day, but I could still sit on the mat and point at people, so teaching was just about possible. :P

If the injuries are wrist, hand, feet, knees, elbows etc, then I find it's possible to train around them (as opposed to back, ribs or shoulder, which I think are extremely difficult to train around). I will train and spar one handed, or one legged. Most important thing is that you're able to keep yourself under control, not slipping back into normal sparring where you 'forget' your knee/wrist etc is messed up (which painfully 'reminds' you!), along with picking trusted training partners who will keep that injury in mind.

Naturally the most sensible thing is to just not train until your injury is fully recovered, but yeah, most of us probably aren't that sensible. ;)

Also you're really picky in regards training partners Can ;) Definitely a good decision healthwise.

Not long after I started training I entered my first competition... I mean it, I think I had about 3 1/2 weeks total training, so 7-8 sessions (got raped of course).
I was in the weight division because I was chubby, everyone else was in it because they injected protein shake into their eyes before bicep curling hatch backs and bench pressing the bus they drove to the comp in.
First match was with a bloke who probably could have crushed my skull but I managed to get a sweep... He didn't like that (I had no stripes, I noticed he checked in the bull pin) so he tackled me across the mat, driving me to the ground, full weight with his shoulder on my ribs. Heard some... Unsettling noises but carried on. Was uncomfortable from there on and I only had 2 more matches before my run was over, the last match the guy actually just sat on my ribs in side-top-mount just to watch my squirm.
As soon as the adrenaline wore off I could hardly breathe... Walking was a chore and laughing or coughing made me want to die.
2 popped ribs, bruising and some fractures... Weirdly oh this is when I got good at Kesa Gatame (scarf-hold) hurt like a bitch but I just kept getting there so pounced on the opportunity. Purple belt now and my coach still regrets teaching it to me.
Took ages for it to come right because I didn't rest it or let it heal properly.

I've had a few over the years. Choosing your training partners carefully is really important. Don't be too proud to say no to a roll if you know it's a bad idea. No 1 priority is to get healed up.