This sounds like a simplified version of the story. I'm sorry if it's completely accurate.
Assuming you can't rectify the fail, just move forward.
Take responsibility for the fail.
You missed an exam and failed a course, which resulted in failing the year. State something like how you learned a lesson about needing to notify people in advance for an absence or something similar.
Just don't blame anyone else, even if you think it's their fault.
If I was interviewing someone and i heard a story about a dean trying to cover his ass, I'd put you on the do not rank list.
Do great moving forward. Many programs will not give you a shot, but hopefully someone will.
Good luck.