I really hope this isn't going somewhere awful. In almost every Korean romance comic I've read, some guy (or sometimes a woman) does something horrific and illegal (assault, rape, attempted rape, threatening someone's family, blackmail, etc.) and NO ONE EVER GOES TO THE POLICE. Even when the police get involved, THE VICTIM DOESN'T PRESS CHARGES, rationalizing it with some bullshit, like "as long as they stay away from me from now on, it's enough".
Aside from my rant, this is just a really tired and cliche plot development that has nothing to do with the actually interesting parts of the story and just serves to create meaningless suspense.
Sadly that horrific stuff is a trope unto itself in a whole subset of television, in Soap Operas, Telenovella, K-Drama, etc.
It filters into the literary side of things as well sometimes. Whilst I love me some drama sometimes, I see the stuff you mention in a story and it loses any kind of dramatic tension and becomes almost Dadaist in its silliness.
There was an era of yuri, where almost every story had the most ludicrous "drama" tacked on, and inevitably one of the leads would either die of a "mysterious disease", get sexually assaulted, or decide they needed a "normal life" and marry some random guy.
And Korean (and some Chinese) wlw stuff seems to be going through that phase right now.
Presumably that's explained in the next chapter, titled "We're Wife and Wife", but it's likely what Japanese lesbians call marriage. Namely one gets signed on to the other's family register in something similar to an adoption and they share the same last name.