If the original source was reliable, and can be found through archive.org or something similar, then the obviously best approach is to replace the broken link with one that works. If the value of the reference can't be determined, but the statement it was referencing is not controversial (i.e. Vermont is a state in the United States) then simply remove the reference, maybe with a note on the talkpage. If it is an "amazing claim" as Will states, then for once he's right - the dead and unverifiable reference leaves the claim unreferenced, and a {{fact}} tag is appropriate.
Nathan