A dangling participle is a wallet chain, cell phone headset cord, beeper leash, purse strap or other long slender device used to secure an object to a person.
A dangling participle is the "straps" that have the tendency to always get caught on another object when you least expect it to, often resulting in a humurous but humiliating yank in the opposite direction of travel (i.e.: getting out of a car, getting up from a desk, etc.).
An exposed penis, generally used when an exposed dick is seen in public.
"Did you see that dude's dangling participle?"
"What kind of church is this again?"