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That's SO something that would happen to me! Personally, I would taste the stock and as long and your foreign object didn't effect the flavor, I would keep it. When using homemade stock (we make chicken stock about every 4 months) I always make sure I bring it to a boil anyway. That's just me, maybe I live life on the edge. ;)
Unless you think the rubber band came into contact with unsafe chemicals or something before it went into the stock, you're probably okay (at least as far as I know about rubber bands). Taste the stock, though--if it was in there the whole time, your stock might have a bad flavor.
I think it was the rubber band on herbs that I threw in there- unfortunately when I tasted it, it was bitter and a total loss, although the cause could be a lot of things. Thank you!
pierino is a trusted source on General Cooking and Tough Love.
Hey, people boil lobsters with bands still attached to the claws with no harm so I wouldn't worry about it too much.
I agree with Pierino. A rubber band is not going to affect your stock at all.