Merriam-Webster has an entry for half-orphan, meaning someone with only one living parent. They say specifically a child, which would match the usual usage of "orphan" (as mentioned in the question), but it might be used of an adult sometimes, either jocularly or by extension. This doesn't distinguish which parent is dead, but could be combined with a further explanation if it matters.
PopSugar: Did Someone Wish Upon a Star? These Disney Halloween Costumes Are Absolutely Magical
Did Someone Wish Upon a Star? These Disney Halloween Costumes Are Absolutely Magical
CNN: The best Halloween costumes for adults: Stranger Things, ’80s and more
Need some Halloween inspo? We talked to the experts about the best Halloween costumes for adults to find out the trends you’ll be seeing on the streets and at the office party this year.
Fox News: ‘Disney Adults’ anger some online after they invent ‘Disneybounding’ to avoid costume ban: 'My personal hell'
‘Disney Adults’ anger some online after they invent ‘Disneybounding’ to avoid costume ban: 'My personal hell'
New York Post: I’m a ‘Disney Adult’ — I tried ‘Disneybounding’ to fight costume ban