Given that the majority of the Conservative party members are in favour of a no-deal Brexit then IMO the next leader of the party will try and force through a no-deal Brexit. It's likely that they will actively do this rather than just sitting on their hands and letting it happen by default.
Possible and likely, if UKIP/Brexit parties win big. If they underperform and LibDem et.al. win big instead, I wouldn't count on it at all. A No Deal Brexit is not the end of history, but having one with a dysfunctional government, bitterly divided Parliament and against the wishes of the electorate is a bridge too far, even for Ress-Mogg and his vermin. He'd resign citing health reasons, I think.
The fact that it's unlikely that the Conservatives would do well in a general election means it's unlikely that they will call one early. Better to limp along with a wafer thin majority and a supply and confidence arrangement with the DUP than be out of power altogether.
As you suggest, their hand could be forced by a no-confidence vote triggered by Labour, but that would be a bold call and could easily result in Tory rebels "unrebelling" and supporting the government in the no-confidence vote.
Suppose five more Tory MPs resign from the party and join the independent group. They offer you a choice: give us another Brexit referendum, or we'll join with the opposition and force a new general election. What would BJ or Ress-Mogg do? What could they do?
If Bremain parties win, I don't see this as too unlikely. Granted, they may lose big too. We'll see in a few days. Yay.
McHrozni