What is the proper procedure when a passenger seat belt becomes inoperable during flight? I was on a Delta flight in Business class on a 777 and during flight the motor of the seat caused the seat belt buckle to pop off the end of the seat belt causing the seat belt to be inoperable.  

This was a completely full flight and the flight attendants were unable to fix the seat belt.  I ended up just tying the two ends of the seat belt together for landing and the crew found that acceptable.

What should the proper procedure be in this case?
The flight crew should have given you a seatbelt extension to fix the connection. And if that did not work, then you should have been instructed to hold on and ask other passengers to hold you down for landing.
Also, if you were wondering why the flight attendant did not move you to an empty the jump seat, is because FAA regulations don’t permit.