I second Come and Hug Me plus:
Empress Ki - The guy falsely accuses FL's father and the father is left to die. There is more, but it's such a huge spoiler that I will put it separately The same guy kills another guy the FL used to love and still very much cares about towards the end of the show.
My Heart Twinkle Twinkle - The ML doesn't help the father of the girl when the house that the father is in goes on fire, ML does it intentionally, because the father disapproves of him
Born Again - a huge spoiler The FL falls in love with the guy who kills the love of her life in the past life and tries to kill the same guy in the present life. Plus for a long time FL was in love with the guy who she finds out later on is involved in the car accident her parents died in.
The following are sort of, but not 100% what you are looking for:
Falling for Innocence - FL falls in love with the guy that was given a heart of her previous lover, so she feels icky about that.
Pinocchio - The FL's mother's is a reporter and by reporting false/ exaggerated news she makes ML's mother commit suicide.
Secret Garden - FL's father dies saving the ML
Shopping King Louie - For a while they believe that the ML is involved in the accident that happened to the FL's brother
The Last Empress -The guy was given a priority in a hospital, because of his money and power, which caused the death of the FL's mother.
Also not really a romance, but
Kill It also has something like this The ML's mentor kills the FL's boyfriend
