There is a poor track record on war against jungle covered countries whose names start with V.
Whether they should have bothered in the first place though, given how corrupt and dysfunctional the regime in the south was, is an open moral question.
Yes, that's called "losing a war," and no serious strategist pretends that politics is not one of the key theaters (if not the key theater) of conflict.
Yes, that's literally how essentially every war ends; some combination of factors causes one side to stop fighting rather than continuing the pay the price in blood and treasure that fighting demands.
There's probably a few somewhere that end because the losing side doesn't give up but fights to the last person, but that's very much not the norm.
How does a country lose a war without losing any major battles? On the homefront first.