1-800-got-junk.
Despite the reuse/recycle mantra so common today, there is a place for garbage. It's not giving it away piecemeal.
Anyone living in that situation, or inheriting it, needs to pay for haul away. If the city finds out it's being pieced out, the city will come after the person. Get it done quickly and move on.
Cold turkey is the way to go in just about every unhealthy situation.