There was a contestant on The Price Is Right recently who fell ill during the taping. After the first one-bid, her sister or some other relative came down to Contestants Row in her place. It was a good example, though, as to why they don't randomly pick contestants, rather the more exciting people.
And, permit me a twist on the original post, but there was an episode of Match Game where Charles Nelson Reilly was late to the set because he forgot to change his clock for daylight saving time. Johnny Olson filled in. (The intro is up on YouTube somewhere.)\
As for the Press Your Luck, it is entirely possible that a returning contestant straddled two seasons, thus the episode would have aired, and have been eligible for prize redemption. (Although someone with their episode guide at the ready will prove me wrong.) However, I would venture to guess that Peter Tomarken was spinning a little story, rather than being entirely truthful.
