I think you may be misunderstanding the context of damnatio ad bestias.

This was not literally "here's a sword, fight for your right to live". You were dumped into an arena and they let loose animals with the intention of them ripping you apart. It was not a trial to save you. It was a death sentence.

Any cases that I am aware of that has someone eluding the death sentence here is probably identified as apocryphal, such as the tale of David and the Lion's Den. Or Bernard Shaw's "Androcles and the Lion" which is a rather nice play.

This was execution much less than a novelty.

EDIT: The play "Androcles and the Lion" is apparently sourced by material from a Greek writer named Apion, but I am not really familiar with his body of work.

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Follow up question - for what offenses would someone merit such a spectacular and presumably ignoble and disgraceful execution, as opposed to a more mundane one by beheading or strangulation or whatever pedestrian means the Romans of the period used?