While I haven't 'killed off' any parents in stories just yet, I have made my 'sudo' protagonist to be from a single-parent family. That said, in my current story, I don't refer to their parents directly at all. However, I am developing my character's backstory, and here I'm looking deeper at their parents' roles and influences on their characters. I've kept my protagonist's mother and made them a domineering figure to help 'define' or allow us to see why they have certain traits and flawed weaknesses.
That said, orphan protagonists have long been with us. Oliver Twist, Tarzan, Harry Potter, Superman, Batman, Snow White, James Bond... the list is endless. This trait (for want of a better word) allows characters to be driven to 'overcome' and 'define' their families, and when it's done well, it is a fantastic device.
Will I ever use a character as an orphan? I'm not sure.