The story
Compile Heart was founded in 2006 as a subsidiary of Idea Factory.
In 2010, the company acquired a licensing deal with D4 Enterprise (the copyright holder of most property rights under Compile) to create new video games based on franchises from the defunct developer. This does not affect the rights to the Puyo Puyo series which D4 does not own and remains the property of Sega.
From Wikipedia’s article on Compile Heart, shared under CC BY-SA 4.0.4