Ok, so they just disappear. Let's think about this. If this system is 100% perfect and never loses tracking, then the signal going dark would be equivalent to a death signal. If not you could exploit that flaw in the signaling system to kill someone and destroy the body/tagging without using time travel (aka the most illegal thing of all).
Whoa, people keep disappearing from the system right after these 3 mobsters abduct them and take them to abandoned buildings!!?!? Someone call Matlock, this it too perplexing!
Ha ha, exactly.
There's gotta be a million easier and faster ways to dispose of someone without your tracking signal being associated with them. Like using a sniper, or poisoning them, or having someone plant a bomb under their car-- you know, things mobsters have been doing for decades