potential energy of an object within a system can change.

And not even an object at 'rest' is at rest on a molecular level. if you take a god bar and a silver bar, put then next to each other for X amount of time, eventually you will get a bar that is stuck together, not because they're squished but because the molecules move, they diffuse.

Another way ithought about it, all forces acting upon an object have to be equal including vectorness and it cant start off with momentum. Thats a lot of specifics. Objects are in motion, we know that the earth is moving, well to the best we got, the earth is moving : ) so when a moving object hits an object at rest that is less than its mass 2 things now move. There's a lot of options for masses and speeds here. The only time 2 things no longer move after a collision is if their momentum is equal. That's really damn specific. So in kinematic terms i believe rest is less likely, but an opinoin it is