How do they work? Are they shock absorbers or some collapsible thing? How do you know they are ok?

More than a decade ago, a car that was driving to my right decided to make a left turn in front of me. Damage to my car was broken headlight while the rear quarter of her car, and rear tire, folded around bumper. Bumper did not seem annoyed.

Recently someone cut in front of me. At first I did not see damage -- the impact was much less severe (damage to the other car was a small dent) as I had time to almost slow down enough not to touch other car -- so I did not exchange info (other driver was rather glad about that). However, later on I noticed I could move my bumper cover towards the car about 1cm, which since I did not see any other damage makes me think the bumper shocks contracted a bit but never came back.