Custom, proprietary, in-house tools that if they ever get ported to consumer use, cost many thousands of dollars.
There are a few ways- the two major options in Blender are shapekeys and frame-by-frame correction. Neither option is great, but there’s really not a lot of good answers here generally. This, among many other reasons, is why there are hundreds of animators working on every major 3D feature 
Another, newer, option is geometry nodes, which allows for a more automatic solution. Check this out:
This system isn’t perfect and still needs a lot of manual tweaking, IMO, but it’s still incredibly powerful and could potentially save you a lot of time.
My personal answer is a combination of geometry nodes, shapekeys driven though RBF drivers, and… avoiding these situations when possible 
Tricky camera work and careful planning goes a long way here