Yeah, especially after they went through, I was rooting for a happy end for these two. But seeing how fragile their relationship is right now (and we do know she ends up in jail), it's looking like we're not getting a happy end for this couple.
I also have an alternative theory that ML may actually have been the murderer and FL is covering for him. But I'll wait for the next couple chapters to see how this conversation between the detective and FL develops

That detective definitely dropped his wallet on purpose so he can have an excuse to see FL again. The author is intentionally creating some sort of progression between the two, but I don't think it will go romantically though.
I personally think the detective will be her saving grace, IF the plot twist is that FL isn't the actual murderer. Right now, the relationship between FL and ML is deteriorating. ML is already convinced she's the murderer and is also becoming uncomfortably possessive of her. FL, in turn, is feeling incredibly suffocated by ML. We're always seeing doubts from both ends whether this marriage is right for them. I think, were nearing the inevitable end of this relationship. ML might even testify against her - his condition right now seems very unstable and weak, I can see him going against her. With no one on her side, the detective will be her only solace.
I believe the detective has a wife who passed away. FL reminds him of his wife, and because of this connection, I think the detective will help FL. As he investigates further, he'll probably find evidence that FL is innocent. I'm thinking Jaeyun's politician father is the real culprit to the murder. FL will be framed of the murder which is why we see her in jail at the start. But I think the story will continue further, with the detective fully solving the case and proving FL's innocence. Story will end with her out of prison, no longer with ML, and will start anew.