NEVER let your body "fall" down uncontrolled, thats very dangerous. ALWAYS keep tension in your shoulders, keep the joint tight into the socket
However, going full ROM on your elbow (180 degrees), shouldn't be a problem.
Hyperextension of any joint will most certainly a problem, but as long as you lower yourself in a controlled fashion you can still go down as low as you possibly can without hyperextending anything.
Whenever you come back from an injury, you should start with very low weight (>20 reps) where you don't feel any pain or discomfort at all and very slowly adapt to heavier weights.
I would advice you to start with something like assisted pullups (of you have access to the equipment) or BB rows or a similar exercise where you can adjust the resistance to a very low intensity
Also, hammer grip chins seem to be easier on the elbow joints than a suspinated grip