This is what's happening when a group of stooges is together.
Look at those stooges over there gaggling.
Gaggling is an oral sex act involving any phallic object, though typically a penis, in which the a person (the gaggler) recieves the phallic object in to their mouth and down the back of their throat (deep throat) while keeping their mouth wide open.
Gaggling is often accompanied by a gag reflex which produces an excess of saliva. The gag reflex must be controlled in order for the gaggler to gaggle on the phallic object.
It is not uncommon for excessive amounts of saliva to run down the gagglers chin, as saliva produced by the gag relfex and cannot be orally contained due to the gagglers open mouth.
Saliva dripped off of her chin as she was gaggling on Rod's man-stick.