From what I understand in television writing it was a constant struggle of "should we write a cliffhanger hoping it gets us renewed" to "we should have some closure in case we get cancelled", since many writers had no idea what would happen.
ENT's trip to 1944 between seasons 3 and 4. Or in other words what must be the writer's "you made us make this temporal cold war cake and by koala we are gonna make you eat it" letter to the execs.
I don't think we know of a case where it convinced a studio executive, but then again we know very little about the reasons why some shows get renewed and some don't.
We do know cases where ending on a cliffhanger helped drumm up enough fan engagement to reverse a cancellation (timeless on nbc is a recent(ish) example for that)