I would imagine the contestant coordinators as well as the production company itself had all the rules written down for the contestants to review and sign off on. Somewhere it no doubt said "During the Money Cards round, your minimum bets are $50, and all bets must be made in $50 increments until the final card, the Big Bet, where you must wager at least half your money."
If a player had only $50 for the Big Bet (I don't recall this happening but then I've not seen every single episode of Card Sharks), they would only have to bet $25, as that is at least half of $50. As Jim would say "Minimum bets are $50 UNTIL you get to the top card..."