The poem is built around a single image: a fire that burns all night and seems to be cleaning something, but isn't really. The speaker calls it "lying," and that word sets the tone. The fire puts on a show of purpose, as if it were scouring a pot or a room, yet the poem quietly undercuts that show.
The last two lines turn the picture toward something more human. Having "nothing / to come home to" sounds like a description of a person, not a fire. The poem seems to suggest that the restless, busy burning is a way of avoiding emptiness. Staying busy all night is easier than facing a place where no one is waiting.
The title, "Fosterage," hints at being cared for, or caring for someone, in a home that isn't quite your own. That fits the sense of belonging nowhere in particular. The mood is lonely and a little bleak, but it is also gentle. The speaker doesn't scold the fire. They simply see through it, perhaps recognizing something of themselves.