Hmm. I don't have a lot, not main characters at least. Parents show up as side characters sometimes-- but they're just there to be awful, abusive, and/or die.
But! From my oldest comic (under this username, differnet site though); Tales of an Executioner. Her name is Tifinie.

A young lady who was abused by her father, birthed a child in a horrific state, and mercy killed it. And given the comic's name you can imagine how that ends for her. But hey! She's sort of the leading lady, even if the comic is mostly a character study of the Executioner.
Another arguably main character parent is Mr.Berry;

The comic is framed as him reading the journals of 3 dead kids-- one of them being his son, the other two being robots, and putting together what happened to lead to all their deaths. He kills the robots thinking it was to avenge his son, however one of the robots was his son's lover so. Oops. He kills himself upon realising this.