I just recently made a pair of pants and shoes in blender 2.91 stable and I have a surface deform modifier on one of the flaps and on the shoe laces to move them along with the rig. The surface deform modifier works just fine in the viewport but the objects snap back to its original possition when rendered in cycles.
Here are some images.
The shoe laces do the same thing. Here is the modifiers for the laces.
I’m not sure what is making this happen, and a second pair of eyes would be great.