PIR (Passive Infra Red) sensors are actually two pyroelectric IR sensors mounted side-by-side with two slightly different fields of view provided (usually) by Fresnel lens arrays. The sensors are connected so their signals subtract. That means any change in sensor signal caused by heating from the image field does not produce a significant differential output signal, nor does any change in ambient temperature. When a object warmer (or colder) than the background radiation enters the field of view (FOV) of both sensors, it will enter (or leave) the FOV of one sensor before the other because the Fresnel lenses present slightly different points-of-view (POV) to each sensor. This POV difference causes a momentary difference in the differential output of the two sensors, which is further processed electronically to "trigger" the PIR sensor head "ON". This action occurs very rapidly because the thermal response of the pyroelectric sensors is very fast.
What happens when the object being sensed is no longer in the FOV of both sensors? The differential output returns to zero. It is up to the PIR sensor designer to decide how long to wait, after the differential signal decreases below a threshold level, to declare that an object is no longer detected. A long delay helps to prevent false negatives, that is, declaring no object is detected when an object is actually in the FOV.
If you take a PIR sensor apart, you can gain direct access to the pyroelectric sensor elements and do your own signal conditioning. However, considerable experience is required for success because pyroelectric sensors are extremely high impedance current-source devices, much like electret microphones which operate on similar principles. Easier to let the Asian manufacturers do all the heavy lifting. Cheaper, too.