I am using Blender 3.6.1. I have a walk cycle with cloth and particle hair simulation (which have been baked) and I used it in NLA. But the cloth and particle hair simulation broke down when:
I tried to repeat the sequence (the simulation broke down when the sequence repeated).
You need to montage all your armature animation in the NLA first, then bake the simulations (the sims need the final, complete character animation, NLA editing applied, as their inputs).
The messed up simulations you’re encountering are probably due to messed up simulation caches, filled with old data created using the original animation.