I still haven't figured out how to capture the invaders. I'm only seeing a way to let them escape.

you need to use an object in your inventory like a collar or something like this

fight and lust them and use collar

There is two ways to capture an invader.
1. Fight them till they are weak of mentality or high on lust, then use a collar in the item menu.
( the chance depends on their mentality and lust)

2. Some has ability to capture in battle, so if you have a character you wanna use to capture an invader, then make sure it has the ability of capture.

Fun fact: You can still capture them when they on no health, as long you dont end your turn. Otherwise they just die at the end of your turn.

Two ways.

1. Using a Collar (buyable, or can be crafted for some cloth) on an invader when they're lower on health. (You can hold on to two at a time, increases by two more for every Prisoner Cell / Binding Cell you have.) Some also have an ability that lets them capture invaders.

2. If you have a Graveyard and an Altar, you can kill them, retrieve the body, and resurrect it as a zombie. (If you don't mind them being a zombie, that is.)

Thank you guys. I figured it out pretty quick after I posted this. There is also an ability that some of your denizens can learn to capture without using items.