Motion sensor door locks

What does that sensor actually do, and how does it prevent someone from pushing a small thing in the crack and changing it to (try to) trick the sensor?

This sensor is called a REX or Request to Exit. The sensor is meant to allow people to leave an area without having to badge or authenticate leaving the area. Your question is good because the idea of pushing something through and attempting to trigger the REX is something that has been accounted for. The devices can be configured to only test a certain range, such as 4 feet from the top of the door.

The best practice is to have the REX aimed at the door handle so that it triggers when someone is actually trying to leave the area, but having the range configured so it should not trigger if someone is trying to stuff something under the door. Newer sensors often utilize IR to ensure that it is not an inanimate object, but a person trying to leave the area.

The combination of having a properly configured REX as well as IR sensors in the REX reduces the likelihood of a vulnerability and increases the odds that the door can only be opened when someone is on the inside attempting to leave.