Half east Asian here, with a bunch of other Asian friend who've had very "east Asian expectation of their children" kind of manipulative & controlling parents. On the legal side I don't know how the paperwork works in HK, I do similar thing exist in Japan (where I'm at) but afaik it have nothing to do with pension, and more to do with health insurance (you can be covered by your parents). There might be a payout if the pension recipient dies that goes to the spouse first and then to the children, so maybe that, or maybe HK is different, but I'd say fuck it, she doesn't have to sign shit, just leave and they can sort that shit out for themselves. its for their convenience they want that, not hers, so the onus is on them.
My mother was quite manipulative too, and what I did was just stopping talking to her at all when I moved out. Blocked everything, didn't tell her where I lived, never reached out. Stayed that way for maybe 3-4 years, and now the relationship is a bit better but I have to remind her often "if you throw your shit again, I will just walk away and never talk to you again". Now that she's in her retirement age, realizing that she doesn't have leverage over me, the attitude is different. Also with your typical east Asian culture, ungrateful young kids are a disgrace but ungrateful adult kids (that never visit now old parents), then people start to suspect the parents are not innocent either; and they usually get aware of that and either reach out or act like you never existed.
Another half Asian friend did the same. For him, his brother gave her mom an ultimatum when he was about to move out for college: we either go to family counseling (therapy) or its byebye forever. To my surprise the mom did go to therapy and now they have a way better relationship, but I wouldn't bet on that to happen for your gf.
From my experience I would just advice to leave them, and ignore them. You can't chose who your parents are, sadly.
As for what you can help her with, something my ex did that soothed the anxiety around it for me was when I shared all this, and she shared it to her mother and apparently her mother laughed and said "well then I can adopt him!" (as in a son-in-law kind of way).
As silly as it sounds, knowing that my (bad) relationship to my parents is not dooming my ability to create a healthy relationship/family, or that there's other people out there than can show me that kindness, was very reassuring. Manipulative parent instill sense of guilt on their children, and that guilt slowly also turn to self-doubt. So as a boyfriend I guess being there for her and reassuring her that her relationship to her parents doesn't define her, and that if she won't be able to go home, she can go home/be with you, would probably help.
Just my 5 cents from my experience,
About the paper work though, take a closer look at it before you decide to leave or do something drastic. There's this story of a girl that was thrown out by her parents and ended up homeless because the parent refused to give her certain paperwork. So a proper exit strategy is good to have.