Caffrey Taffy Company were a Taffy Company.
It was owned by Mr. Caffrey who passed away before the series began. His body is seen in his customized casket Mort created in Human Flesh when Gene delivers his burger to him. More about Caffrey's backstory is revealed in Sea Me Now.
In The Belchies the factory is scheduled for demolition. After hearing stories that the factory is filled with gold bricks from Teddy, the kids decide to sneak in to get the gold. This all goes wrong as Louise ends up getting trapped while the demolition is in progress. Eventually they escape and it is revealed at the end that Teddy's stories were true.