Flights are tracked by radar and by transponder. The appropriate thing to do is just flag the flight with a discontinuity error but otherwise operate normally. This happens with other statuses like "radio failure" or "emergency aircraft."
It's not something you'd see on a commercial flight, but a private IFR flight (one with a flight plan), you can actually cancel your IFR plan mid flight and revert to VFR (visual flight rules) instead.
Some flights take off without an IFR clearance as a VFR flight, but once airborne, they call up ATC and request an IFR clearance already en route.
The system is vouchsafing where it does not need to.