Laurefindel
Legend
That's what the chase rules are for, with different checks to see who catches up with who, and who manages to run away from who. At least that's the "pulling something fancy" part. You can use the chase rules in the DMG or houseruled ones, but usually chase rules are a subsystem different from combat. Then, the question is when does a combat stop being combat and when does it start to be a chase.Sure.
But if you are in melee, and you are running away from someone who moves at the same speed or faster than you do, you don't get away unless you pull off something fancy.
If everyone is move/OAing, then the fleeing foes are killed. You could eyeball how far they run if it matters. If it really matters (if the foe gets 100' away the world ends!) do the mechanics of each round.
The players are free to let fleeing foes flee. If they don't, well, you can solve "they won't get away" without mechanics, no?
My take is still: as soon as one wishes to escape, at the start of their turn.