Most of these systems have multiple short-range transponders spread around the car. Some by the doors, some inside, and sometimes one in the trunk (so you can't lock your keys in the trunk). The way the system works in that each "transponder" is really just an LF (I think 120 KHz) RFID transmitter that interrogates the key. They key, when interrogated, will transmit a reply back to the car on 433 MHZ. The 433 MHz is the same radio link used for the remote lock/unlock buttons on the remote. The car usually only has a single 433MHz receiver; sometimes the same receiver is used for listening to the key's transmissions and the tire pressure monitoring sensors. Since the 433 MHZ transmission is longer range, they use the 120KHz RFID to get the short-range "proximitry" type effect.
Note that the key is very much active; the system will not work when the battery in the key dies. Luckily, most (all?) cars have a backup in that you can pull an emergency metal key out of the keyfob that will allow you to open the car door, but not start the engine. Somewhere inside the car, one of the transponders can activate/power the key via RFID if the key is close enough. On a Subaru BRZ, you just push the "start" button with the keyfob itself! This lets you start the car with a dead battery in the fob. Also note that the key is only needed to start the car (you can chunk it out the window and keep driving with only a message on the dash) since cutting the engine while driving may be dangerous.