Treating this question as: how could a low-level enemy plausibly escape from the PCs?
Some possibilities:
Enemy has superior movement to the PCs. For example, he can fly off into the forest.
Enemy has superior senses to the PCs. He runs off into the smoke / fog where the PCs can't see him to follow.
Enemy has prepared terrain. He runs off down the corridor. If the PCs try to follow him, they trigger a falling rubble trap. Or he simply slams a door behind him and it locks.
Enemy is a respected citizen of the town and the PCs have no proof of his guilt. He calls for the town guard and demands their protection.
Enemy has a one-shot item, like a potion of Invisibility.
I use moral checks at 25% and 50% HP, also if there is a group mobs and 50% are drop in a round, I do a check.
Same situation, but the other direction. I have seen groups TPK because, "By the numbers, we can't get away."
In PF most things that can beat you can also catch you. Or at the very least, keep up with you.
That's why PF introduced the chase scene rules. I think it is in the Game Mastery Guide.
Basically it provides a semi-random collection of jumped over a fence, rolled under a cart, ducked through a dark alley way, etc... type occurrences along with a DC for performing the action.
So the fleeing dude makes DC=15 acrobatics check and rolls under the wagon. The pursuer can take a missile fire (or spell) shot while falling further behind OR can also try the acrobatics check to try and keep up.
No it is not perfectly realistic. However, it is playable and much better than assuming every medium sized person in the world runs at the same speed. So of course they will just keep pace with each other until one gets fatigued and drops.
I use the video game method, if you get to the edge of the map you escape.
Edit. Granted there are situations where this doesn't always apply. Fighting inside a small building for example. In that case I adapt, the NPC may be forced to fight to the death if cornered or may try to surrender.
So do you guys think chase mechanics would be a good addition to make important villains potentially be able to run away?
Yes, if used in moderation.
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Chase rules depend on the group. I have a player who hates them because they tend to turn spells off and are geared more towards physical skills and stats. He feels the chase rules take away too much of his agency. Personally, I dont mind having a game element where martials have the edge.
One thing GMs often forget about is terrain and combat setting. Sometimes the enemy gets the drop on the PCs or gets to place a well thought out ambush. In a fantasy world, that well thought out ambush should have a pear shaped clause. Difficult terrain, fogs clouds, seal-able doors, easily attainable mounts, etc. Also, villains are likely to use their minions especially cult like ones to help distract the PCs while they get away. Of course all these elements are easily overcome by PCs at higher levels but the NPCs also gain better get away abilities. Occasionally, things go in the PCs favor and they get the ambush and in such case the villain may be boned and if so you should let the PCs have the win.
As far as morale goes, I usually try and put myself in the NPCs shoes. Mindless monsters are more likely to fight to the bitter end. Intelligent foes however will weigh the likely-hood of capture and sentence. Petty crimes and such they will probably surrender. Fanatics and the evil characters may choose death before defeat. Most NPCs are not above running though.
Caltrops, smoke sticks and all variety of low level spells can help to escape. Or to stop someone trying to escape.
... I have a player who hates them because they tend to turn spells off and are geared more towards physical skills and stats. He feels the chase rules take away too much of his agency. ...
Guess I don't see this. We've always found spells the easiest way to deal with the chase scene. A lot of spells will carry you right through most of the blocks. Even if it doesn't, the other guys challenges also slow him down keeping him in spell range for longer.
We usually found the monk, rogue, or ranger could breeze through the chase (which makes sense to me).
The heavily armored, low skill, and slow characters had a horrible time with the chase (which again makes sense to me).
The primary caster could blow through with a dimension door, fly over with fly leap several obstacles with jump, hinder the other guy with things like grease/slow/entangle, spiritual ally, OR just blast the heck out of him.
But we really don't bother with them too often except for moderately important bad guys or if the players try to run.
To quote Batman, "Criminals are a superstitious and cowardly lot". Why die when they can let their lackeys die for them? At low levels, the best option is for the non-magical escape route. Don't allow the bad guy linger too long in the fight and get trapped by inventive characters... let him feel that the tide of battle is turning early, and have him run before he's personally challenged.
Have him duck down a secret passage with a (minor) trap that discourages the party from running like madmen after him. Or perhaps have him duck down a door with an iron portcullis that falls down before it, slowing the pursuit. Maybe even a nifty deliberate trap floor that opens up beneath him dramatically.
If the group is dogged, lead them towards a path that splits up... and no matter which way they choose, it's the wrong route. However, don't discourage them - reward them for their tenacity, by having them discover something of value or a piece of vital information down whichever passage they do go.
I usually decide what Will make the baddies run when i design the encounter.
Like goblins Will run if main melee guy isent Down in 3 turns, if more than 6 of them Fall in the first turn or when there ogre ally goes Down.
In my games, I let PC's run away any time they want. I've told them though, that when they do, something important and bad will happen, representing a campaign level setback (the severity of which is determined by how important/difficult the encounter was). To successfully run away, the players must be unanimous in their decision. Seeing as there are usually 6+ players present, that's often harder than it sounds.
Reading this thread, I may introduce an inverse rule of this. Bad guys can run away automatically (maybe 1 round of actions/attacks from the players to try to stop it), but if I do that, the PC's score some kind of campaign level advantage. Like they know enough about the villains next move to preempt it entirely if they choose.
Hire an extraction specialist. I stated up at one point a Hunter built solely to either kidnap someone or rescue someone. I think it had access to about a 300ft speed or some jazz.
Different enemies have different responses.
Throw themselves at your mercy and drop their weapons. Counting on your party to not be murderous evil doers.
Dropping weapons and running. Counting on your party not being murderous evil doers.
Running full tilt and hoping you don't follow or can't keep up.
Hamstringing the biggest fighter and running away while you fight the guy who can't run. (Yes my NPCs can be a-holes).
My favorite is stabbing a random bystander that is not looking at them screaming, as they drop the dagger and point at you that your a murderer. I had a pirate do this in Skull and Shackles. She was losing a fist fight below decks not all of the other pirates had woken (they were starting to) so rather than go toe to toe with the monk kicking her tail she rolled under a bunk with someone it it stabbed the guy who was still a sleep and the screamed bloody murder that the PCs were trying to kill everyone.