Looking to spice up your game and get your players really invested in stopping a bad guy? Just tired of rolling up new villains that your PCs kill one after the other? Well, for both of these you can save yourself a lot of time and effort by simply introducing the concept of the one that got away. How does it work? Well, basically, before the villain gets grievously wounded to the point they can't escape, you have them leave the scene. They can then lick their wounds, recoup, and come back even stronger. Let's look into some ways to pull this off.
Disengaging is Key
The hardest part of this, especially in combat situations, is pulling off the disengage. Why? Well, odds are your PCs will chase the villain. Players don't like the idea of the villain getting away because it can mean a number of "bad" things for them from not getting full XP for the encounter to having to watch their back. Because of this it is important to have your villain have an escape plan, and have that escape plan account for the obvious - and less obvious - ways that the person might be stopped.
Depending on the character themself and the setting for the world how this works might change. For example, in a high fantasy setting a mage might activate a contingency teleportation spell to escape while in a high tech future setting maybe the person teleports out to their ship. No access to teleportation? Smoke clouds work well. As do dopplegangers. Escaping in the mix while a large group guards/fighters for their side rush in can also work.
No Body = Not Dead
If all else fails you can fall back on the old trope of serial comics and TV shows everywhere. If you don't see a body, the person isn't dead. For this reason you have the person die in a way that keeps the bodies away from the PC. Maybe the PC hits the villain but in the process the villain falls over a rail and into a bottomless chasm, or into an explosion, or just into the abyssal dark. Either way, if you can prevent the body from being seen you can simply say "she didn't die" and take some time to come up with ways the villain survived later.
Cherry Pick Your Villain
These kinds of villains should be smart. They should be planners and plotters. There are two reasons for this. One, these are the kind of villains that are the most awesome to see them recur over and over again. Two, these are the kind of villains who are likely to have escape plans set up and ready to go. Also, this is a villain you want to use as a set piece for a variety of sessions and adventures. Because of this you want to take your time in making them, take your time in making their plans, and use them carefully.
The Pay Off
For those of you wondering why this works and why you want it, the pay off is huge. If you can establish a villain who gets away, or better yet who sometimes wins, then you get the joy of seeing the NPC and PCs developing a relationship and one that isn't cooperative but rather adversarial. Do it right and you can even see the characters develop respect for each other. Build the villain right, give them their own motivations, and it is even possible you'll be able to set up situations where the villain and the PCs work together against a common foe. All of this helps add drama to your game. It helsp to add motivation to the actions of the PCs. Most of all, it helps bring the game to the next level and that is an awesome thing to have.