To be fair, a realistic resolution might give the group a ranged attack before the other guy finishes his move.
What wouldn't be fair would be to allow them to close and attack a person who moves at least as fast as they do, in mph or fps, and who started running first.
Now, in a "realistic" system, how far should he be able to get before they get a step-and-shoot? I'd probably base it on how much he beat their initiative by. For every five points or fraction thereof I'd give him 30 feet. That lets him finish his full quad move run if he beat them by 20 points on a D20 roll, as the extreme case, or get a single move of 30 if he beat them by 5 or less.
I would always give him the single, at a minimum, because he won the initiative and that has to count for something.
Now if he beats them that way (5 or less) so he's just 30 feet away when they react, why can't they Charge and take him down?
Well, if you're trying to de-segment time and movement by increasing the granularity, you have to increase it for everyone the same amount. You can't give him a quarter of his action and then give them a full action in the middle. If they pursue, they're moving at the same speed he is and won't be able to close that gap until something happens to break his stride.
So if they pursue they pursue at the same speed, and they end the round as far from him as they began.
As for chase rules: I haven't seen a good set for D&D.
In one game I was playing a Barbarian (base move 40) being chased by an Ogre (base move 50). Drove the DM nuts, because it was obvious that he was going to outrun me on the numbers alone, but he couldn't work out how to actually bring me down.
I began with a Withdrawal and a full run away, 160 feet. He followed with 160 feet of movement of his own, which is less than a quad/run for him but more than a double/hustle. That meant that he had no Charge, no Dex, and therefore no AoO when my character Ran again next round.
So he ran past me next time, to cut me off, and to theoretically build enough of a lead to snare me after a Double eventually. My character changed direction, again leaving him more than a triple move behind.
We zig-zagged across those fields this way until I manage to reach the rest of my group. He broke off rather than run into a situation where he was outnumbered like that.
But with or without a safe haven to head for, we could have played tag out there all day, or at least until somebody failed a CON check from all that running, and he'd be "it" all day.
No, hot pursuit in D&D is Zeno's Paradox in action.