This is something that thankfully only happens occasionally. Although when I worked in vfx it was more frequent. At Blue Sky, sometimes a supervisor would get too busy and have to hand a shot off, or someone would leave or get sick for a long while and the shot needed to be finished. Taking over someone else's shot is challenging because people animate in different methods and often with different movers. What you do will depend on the state the shot is in. If it is rough blocking, you can clean up the poses a bit and just use it as your own file, or if you prefer, make a playblast, and pose out your own file using the playblast as reference. If the shot is in splining then you have to use what is there, figure out what movers they used and work with it.
It can be a nightmare deconstructing how somebody else’s animation mind works but the supervisors will understand this and give you some extra time to figure those things out.
I had to do this once on Horton Hears a Who with a shot of Vlad climbing up a tree. The supervisor had great blocking in, but his methods seemed messy to me and I ended up just making a playblast and using that as reference. Of course, he put extra pressure on me to make it good because it was his shot originally.
On Iron Man 2, I got a shot of Iron Man being tossed into a car. The animator had put keys on all sorts of movers I never used, so I couldn’t figure out where some movement was coming from until I spoke with him. In another shot on the film, an animator had done a pass and they changed directions with it. I ended up re-working the shot, and basically starting over from scratch, after trying and failing to use the data.
The best tip I can give is to speak with the animator who was working on it right away. Ask them how they went about it, what movers they used, and ask the supervisor what he wants to do differently than what is currently there. Just don’t get easily frustrated if someone takes your shot, or feel too bad when you have to finish a fellow animators’ shot. It is not something that anyone wants to do. But it is part of the job.