At the very beginning of the first 2016 republican primary debate the candidates were asked if any one of them would not commit to throwing their full support behind whichever candidate won the primary and were asked if any one of them would not rule out a third party run.
I have not watched primary debates for previous presidential elections so I'm left wondering if this is a common question.
No it isn't a common thing to ask candidates, almost every candidate won't run as a third party if they lose the nomination. What happened during the republican primary debate was a pretty blatant attack on Donald Trump. Part of the reason for the question is Trump publicly mentioned running as a third party candidate in the last election and hasn't said he won't try it if he loses the republican nomination. Running as a third party candidate is a big deal, because it tends to split the vote for the more closely aligned major party and all but guaranteeing a victory for the opposite party.
pretty blatant attack. Obviously the question was directed at Trump, but as you explain in you answer, it is an important topic and Trump had not previously clarified his position, leading to legitimate doubts about what he could do. After all, they were in the debate to publicly explain their position in all of the topics related to the presidential election, weren't they?