I have information about the closest thing to it, which is people being thrown into the arena by a guard, ordered by the Emperor. This is a quote I found in a paper and I chased down each reference and it's the same thing basically, the Emperor is wronged in some way by someone. They or their loved ones are tossed into the arena as a punishment/execution. Here's the quote.

"The blood lust of the spectators, populus and emperors alike, the brutality of the combat, and the callous deaths of men and animals still disturb modern sensibilities. Certainly, Rome was cruel. Defeated enemies and criminals forfeited any right to a place within society, although they still might be saved (servare) from the death they deserved and be made slaves (servi). Because the life of the slave was forfeit, there was no question but that it could be claimed at any time. The paterfamilias of the family had absolute control over the lives of his slaves (and little less over those of his wife and children). In the army, decimation was the consequence of cowardice. The plague was ever present, as was the capricious whim of the emperor, who might seize a spectator from the crowd and have him thrown into the arena (Suetonius, Claudius, XXIV; Caligula, XXXV; Domitian, X; Dio, LIX.10)."

Perhaps someone with more indepth knowledge knows of specific incidents, but all I found were always intentional and by a guard throwing or the emperor pushing someone into the arena.

The Suetonius sections can be read in detail here: https://www.gutenberg.org/files/6400/6400-h/6400-h.htm

Dio section here: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/59*.html

Original thing I found that lead me to those (not really a source): http://penelope.uchicago.edu/~grout/encyclopaedia_romana/gladiators/gladiators.html