From what I've seen, these are some categories obsessive bottoms fall under. Obviously this is a pretty rare trope so not everything can be categorized.
The manipulative two-faced "green tea" type. Usually uses their cuteness/softness to make their top want to protect them out of their own free will. Manipulates their top and the top's close ones to isolate them and usually stalks them to some degree to be in the right place at the right time to appear to be the perfect partner. The top eventually finds out their true nature but usually this is well into when they are deep in a relationship and by then the top is too invested to break free so just learns to manage their partner's obsessiveness. (Ex. 反向驯养, The Method Messiah(also kinda #3 as well, might change this depending on the remaining chapters))
Basically the same as the usual obsessive top but now they are a bottom. Domineering, sometimes sadistic, usually significantly more wealthy than the top, has some sort of power imbalance with their top, etc. Usually their tops are pragmatic of their position and just accept their unhealthy relationship with their top if it puts a roof over their head and food on the table. As a result, the obsessive bottom, while still insecure in their relationship (thus sometimes trying to lock up their top), usually doesn't resort to violence like a lot of obsessive tops do. (Ex. Boss, Bxtch, Baby. The Taming)
A delusional bulldozer type that charges forward and never stops. They brazenly attempt to manipulate their top into loving them and the top is super aware of this but can't help falling anyway. They don't "stalk", they "watch over". Their top didn't "run away", they are taking a little vacation. Basically anything their top does can be twisted into something romantic, much to the top's annoyance. Sometimes this type is for a comedic story and sometimes for a more serious one. Can work for both atmospheres. The most common type that I've seen. (Ex. 바닥에서 한 뼘, Even in Your Death)
A bottom that is obsessed with their top out of hatred but also can't help their attraction to them. For whatever reason, the bottom absolutely hates the top but the fine line between hate and love means that they love their top just as much as they hate, and eventually the love wins out. They previously wanted to be a constant thorn in their top's life but now they can't bear to be separated for another reason.....Most likely candidate to be in a bathroom somewhere going "Don't forget...this is for revenge😡" or something while thinking about their top's touch and how they can permanently mentally imprint themselves on their top's psyche. (Ex. Ignite the Dawn, Checkmate)
My personal fave is the manipulative green tea type, I'm always sending suggestions to 7seas to translate 反向驯养 :p