Paul's hit the nail on the head. You only wear a squawk so ATC can see you with their secondary surveillance radar. Since the radars don't have the range to extend out over the Atlantic, Pacific, sparse parts of Africa etc they can't see your squawk and you're on a Procedural Service. As FIRs are regularly crossed on those sort of flights it is normal to squawk 2000. Once you come into range of ATC they'll allocate you a squawk relevant to the controlling agency and at an appropriate time you'll be put back under Radar Control.
In the not-too-distant past the Procedural Service was all controlled using specific speeds, position reports etc and a WW 2 plotting table. Nowadays they can actually 'see' you from your ADS-B/C and just send text messages over CPDLC, instead of scratchy HF