Depends on the ride. Some, if you don't raise the minimum you either put in your own to get to that, or you don't ride. I signed up for a 'best buddies' fundraiser this fall and the fine print said that if I didn't raise the minimum ($900) that the balance would be billed to my card. I'm hoping to at least raise a little of that so It isn't all on me. But I ask my friends for donations for the Livestrong ride in August, so not sure if I'd go about asking anyone for money for the fall one.
Look on the site, there is likely information there telling you how they will handle it.