Well, we now know a pretty decent case where this happened. Melinda Warren's story (the great Harry Potter one) where her friend Parvati had a bid to Slytherin and had to later turn it down, and Melinda went bidless. Now, Melinda was dropped from the system before pref, so it's a little different. However, all Melinda had before that was Slytherin, so she could have (in theory) had that bid that Parvati had taken
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