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Their only real appearance in SMG4's bloopers was in Boil the Big Bully. In this blooper, they are in charge of the smaller Bullies. One Big Bully called a meeting for the Bullies to tell them that there is an impersonator in the area, that being Steve. After Steve is kicked out, he tells the Bullies to enjoy the new territory and to not disturb the boss. These Bullies are lead by the Bully Boss.
It is possible the Big Bullies died with the other Bullies and Bully Boss when SMG4 tricked them with a big cookie, with the Bully Boss being an exception because he died while fighting Mario.