It relies on the tiny bit of drag that the satellites experience from the super thin atmosphere up there. As they get lower and lower the atmosphere density increases so the process accelerates gradually toward reentry. Satellites today typically save some fuel to lower their orbit partway at end of service life and then let drag take over from there. Some newer concepts inflate a balloon or other appendage at the end of satellite life to provide a larger drag cross-section and speed up the reentry process.
thanks for that information.