Ive heard this from one of my friends, who regularly flies EK BOM-DXB-BOM route, that very recently his EK flight had got severely delayed at DXB (He was waiting in BOM for arrival) due to tech errors. The delay was 5 hours plus and yet no signs of arrival. Finally when they came in, there were two EK 77L arrivals back to back.
The first flight was for picking them up, and the other was the routine flight which was also full.
When he boarded, he spoke to the crew members. They said the first flight (on which he was there) was re-directed from SYD to pick up passengers at BOM since the flight was not full, and the other arrival (which was on time) flew in the cockpit crew which would fly the Sydney re-directed flight from BOM to DXB since the other crew was out of hours. The original crew then flew like passengers.
Now, can this happen? As far as i know, an airline may not have the authority to do this. But given EK and their presence in Indian markets, i do see this as a possibility.