Importance of Rug

This is a rug on the floor of Room. Jack and Ma move it to do their walks around the track. Ma wraps Jack in Rug when he pretends to be dead and makes his escape from Old Nick. After Jack and Ma move into their own apartment, Jack wants to have Rug back. To Jack, this and the other possessions from Room provide a sense of security. To Ma, they represent her captivity. Ma eventually allows Jack to keep Rug but insists he leave it out of sight in his closet.