When you furl something made of fabric such as an umbrella, sail, or flag, you roll or fold it up because it is not going to be used. An attempt was made to furl the headsail. a furled umbrella
To draw up or gather into close compass; to wrap or roll, as a sail, close to the yard, stay, or mast, or, as a flag, close to or around its staff, securing it there by a gasket or line