In the film both Vinnie and Pizza the Hutt threatened to kill Lone Starr and Barf if he did not pay his debt of 1,000,000 spacebucks to them by tomorrow, effectively making Vinnie and Pizza responsible for Lone Starr and Barf accepting King Roland, the king of Druidia's request and setting in motion the events of the story.
By the end of the movie, Pizza the Hutt is killed when he was trapped inside his limousine and ate himself to death. It's unknown what became of Vinnie afterwards, although it's likely he either became unemployed or was made the new head of Pizza's organization.
The name for this character was actually inspired by DeLuca's brother Vincent Thomas DeLuca. Rudy being longtime friends with Director Mel Brooks, asked this as small favor to pay homage to his brother.