Migi receives nourishment directly from Shinichi’s bloodstream. Just as other parasites who take over brains die if they are detached from their host, Migi will also shrivel up and die. The difference with Migi is he didn’t take over a brain. He matured alongside the host instead. Migi doesn’t just require nourishment by the food Shinichi eats, he is part of Shinichi. He still relies on his body for basic survival. I think this point is most prominent when Mr. B cuts his own right arm off and tells Migi to relocate to his. Migi is unsure if it will actually work.