There are several ways to get the ID out there without being heard at voice modulation levels. Quite often the Morse ID is transmitted without PL/DPL (CTCSS/DCS subtone), so if you have the channel programmed with PL/DPL, you wont hear the station ID.
Then there's the ID that's transmitted at PL/DPL (subtone) levels but not on the same subtone frequency as a PL or DPL, so if you're in PL/DPL mode, you won't hear that one either. If you're not in PL/DPL mode, it'll just sound like a dead key for a second or two as the ID is passed. If the station is a repeater, these subtone ID types can also be transmitted during the repeater hang time, so you really never know that the ID is going out.