The only time this has happened to us is the week of 9/11/01. We were scheduled for the studio on Saturday (9/8) night and then we were moving to a 2-bedroom (it was actually a lock-off unit). We "moved" (opened the door between the units, really)as scheduled on Sunday. I had went down early with some friends and the rest of my family was arriving Sunday evening. My friends stayed in the 2nd bedroom (our studio the evening before) and they were scheduled to leave on 9/13. My family and I were staying until 9/21.
As you know, all flights were cancelled after the tragedies in NY, DC and PA. Although they checked their flight before leaving for the airport on Thursday, it was cancelled and they were forced to come back to OKW. We had planned to go back into the studio (the second bedroom they had been using) for Friday and Saturday night and then back to the two-bedroom on Sunday morning. (I know, it's complicated, but we were trying to save points!

) They were unable to leave Orlando until Sunday morning - a hurricane had stranded planes in the north to add to the already chaotic situation.
Disney was great, though. When we explained our problem, they asked my friend to show the front desk their plane tickets and we were able to stay in the two-bedroom, giving them the use of the studio until they left on Sunday morning. We incurred no extra point usage for the extra 2 nights we used the larger part of the unit and my friends did not have to pay for a room somewhere else.
I understand that OKW was only 40% occupied at the time, so it was relatively easy for them to do this, but I was really grateful that they were so accommodating (though not surprised).
No one needs to "sell" me on Disney. I am a fan for life. But they were extremely gracious and kind during a very, very difficult time. They're tops in my book.