Green's Parents are minor characters that were first introduced in the Firered and Leafgreen Arc.
In the beginning of the FRLG chapter, Green talks to Silver about how she's going to meet her parents for the first time since her abduction, and how they've been searching for her for a long time.
While on the dock, the parents see their daughter aboard the S. S. Anne, and rush happily on the ship to meet her. However, they were unaware that she was being attacked by a mysterious figure, and ended up sinking into a hole of darkness when they tried to reach her.
Green mentions them near the end of the Emerald Arc.