This really applies to analog radios only, but it's referred to as squelch tail eliminator (STE) by some of the manufacturers and consists of a burst of the CTCSS subtone at the end of transmission encoded so as to allow the receiving radio decode it as a cue to turn off the receiver audio. As long as the receiver audio turns off before the carrier drops, you hear......nothing. It can also be done by simply turning off the transmitter subtone about a half second before the carrier drops. The receiving radio will simply turn off the audio because the CTCSS subtone is no longer there. There are repeater systems that turn off the repeater transmit subtone as soon as the carrier coming into the receiver from a mobile or control station drops. That way, the repeater hang time is still there, but there's no CTCSS subtone being transmitted, so the receiving mobiles and control stations turn off the receiver audio and go silent. When this is done, even radios without STE will go silent with no squelch tail just because the subtone is no longer there to keep the audio open.
Digital systems can't decode noise, so they simply turn off the audio when there's no longer any digital intelligence being received.