In Yume Nikki, there are enemies known as 'chasers' that can catch you and trap you in inescapable places, such as the Toriningen. There many are enemies much like that in Yume 2kki. Here is the list.
Shadow Woman/Witches
These are the main chasers in Yume 2kki and are equivalent to the Toriningen from Yume Nikki. They are found in many places in the dream world and will trap you in a small area or maze you can not get out of. They can also sometimes appear to be flat (like a cardboard cutout) when traveling left or right. On Uboachan.net and a YouTube video, she has also been referred to as "PMS-chan".
Clowns
Exactly the same as the Shadow Woman, but in a more creepy clown style. There are many throughout the dreamworld, some of them sane and some insane. The laugh they let out when they catch you sounds exactly like Smile-san's laugh. On Uboachan, somebody has nicknamed one of the clowns Pennywise.
You can find Pennywise (who is sane) in one of the rooms of the gray building in Guts World. He takes your money if you use the chainsaw on him. If you chainsaw him many times, he will chase you, and if you've been caught, he will trap you in a closed area. Even if you escape you're not safe, all the chasers, including the previously calm ones, will be after you throughout the whole dream world. They will pop up in places they are not normally found in and often moving faster than they supposed to... They won't be calmed if you wake up, the only way to calm them is to get caught by a chaser.
Shadow Bird
Doesn't exactly chase you, but moves at an average speed and traps you if you interact with it or it catches you. On Uboachan, someone has nicknamed it Crowdude. It appears to be based on the Mothman.
Shadow Gloop
A blob that actually chases you, but is way too slow to even worry about. Has a slight resemblance to Swalot from Pokémon. Someone on Uboachan has nicknamed it Fats.
Shadow ???
A big enemy that chases you, but is very slow. On Uboachan, it has been nicknamed Gonks.
Scary Face
Floating faces with mad eyes and sharp teeth. When they reach a dead end, they bounce up and down. If you get caught by him, it either brings you to a secluded area in the shape of a cross or traps you in a table surrounded by knives in Blood World.
Bug Girl
The enemy that chases you when you chainsaw her to get the Bug effect. Keep in mind that if you try to use the Invisible effect, she won't be able to see you, but will begin to will move in a pattern similar to Dogboa, making it harder to evade her.
White Eyes
Found in Geometry World in the maze. Simply sends you back to the entrance of the maze.
Evil Bugs
These appear in the Red Bug Maze event. They block you from certain exits and function in the same way regular chasers do.
Robot Guard
These used to appear primarily in an event in the Pokémon World, but also apparently guarded the Fairy effect. A single one can now be found at the Highway (still guarding the Fairy effect) and one also appears in the Baddies Bar. The Invisible effect is needed to get past them.
Teacher
Found in only the School and functions similar to a chaser. Using the Glasses effect near him reveals that he's actually a ghost. Although normally he won't harm you, using the Bike effect in the School causes him to become insane and chase you, and if you get caught you'll be transported to a staff room where you'll be in what appears to be 'detention' while he scolds you. Trying to walk away causes the Teacher to jump up and force you back to your place, so your only means of escape are waking up or using the Eyeball Bomb effect. Chainsawing him causes him to turn into a ghost and follow you, although he is very slow. Getting caught causes you to wake up.
If you escape the room, you'll actually end up walking out of the last classroom in the School, the most unkempt classroom of all. Getting caught by the Teacher again while riding your Bike sends you back to detention, but this time he'll already be a ghost and chase you (and oddly, he's even more transparent this time).