Let me explain Phase Lock first: When two objects of non zero mass occupy the same space but have zero energy (no velocity).

Do they bump forever with zero velocity resolution vectors or do they just stay locked together until an outside force interacts?

In my home brewed engine, I realized that if I loaded a character into a tree and moved them, they would signal a collision and hop back to their original spot. I suppose I could fix this by implementing impulses in the event of a collision instead of just jumping back to the last spot I was in (my implementation kind of sucks).

But while I make my engine more robust, I'm just curious on how most other physics engines handle this case. Do objects that start in the same spot with no movement speed just shoot out from each other in a random direction? Or do they sit there until something happens? Which option is generally the best approach?