A three-phase motor will not start if one or two phases aren't connected. If while running one or two phases "drop out", it will continue to run for awhile, but will eventually burn out, unless...
The incoming single phase line is in series with all three contactor contacts. For example; Incoming supply line to the top of A phase contact. From the bottom of A phase contact to the top of B...
With a single phase motor driving a 3 phase generator. It is possible to do it electronically, but that would more expensive and the more the power requirement is, the more expensive it would be.