The preexisting unhealable wound
This trope exists far outside of the world of TV. It’s an archetype that we find across genres, cultures, and media. You see it in all the most complex characters, and it is usually the single motivating factor in every decision they’ve ever made, ever. The unhealable wound can be physical, but it’s usually some psychological trauma inflicted long in the past, but that is still prevalent in their behaviors and decision making.
Of course it varies, but for female characters it’s often abuse at the hands of a male loved one – rape, child abuse, domestic violence. For men, it’s usually something terrible that’s happened to their wife, but sometimes it’s abuse, as well. The past events may not be readily part of their current situation, but the horrible memories stay with them, and it informs how they live their particular lives.
This past unhealable wound offers the opportunity for the hero to be tortured, drink a lot, and sometimes just be a giant jerk. All the terrible decisions they make in their lives can be drawn straight back to “the thing” that happened.
The wound often symbolizes a loss of innocence or the destruction of a perfect ideal, and suffering through it proves the tenacity and mettle of the hero. The character not only uses the wound to excuse their bad behavior, they often draw strength from it (think Harry Potter and his scar).
Examples: House of Cards, How to Get Away With Murder, Arrow, and Game of Thrones