The short, narrow strip of fabric attached to the outside of an umbrella. When used, it furls and tidies the fabric into neat folds and keeps it from flapping, taking up space and wetting those around it. Often it has a snap on the end that connects with its mate when the cord is in use. More modern umbrellas use Velcro instead of a snap.
Sue: Hey, use your umbrellical cord, man, that umbrella is all dripping on me.
Pete: Sorry, I can't, the snap ripped off and I can't afford another one right now.