It has happened, but it's pretty rare. 90%+ of the time the player will get 6+ games.
One way to look at it: "The DoPS is planning to give you 6+ games, do you have any explanation for your actions that would cause us to reduce that suspension length?". In the case of Kassian here I think it would be difficult for him to argue mitigating circumstances in the incident.
In some past incidents the DoPS has apparently accepted some level of mitigating explanation from the player and reduced the planned suspension.
I think there are certainly mitigating factors.
Not huge mitigating factors, but they are there. Notably, Cernak wasn't injured, and it's reasonable to assume that he's trying to rejoin the hockey game and stop having a melee 100 ft from the puck.
I think you take Skinner's 2 games, multiply that by four or five for suspension history / notoriety / bad press the play is generating, then you give him 1 or 2 games back because even though he made a shit choice, he's trying to go play the game (factor two; acting with recklessness and negligence is better relatively speaking than acting with premeditation and intent) and he has no chance to kick if Cernak isn't f***ing with his skates or the official looking right at the play calls Cernak for holding two Oilers players away from the puck for over three steamboats (factor three; aggravation).
It's the same as a murder trial; there is no arguing that Kassian had a guilty action (Actus Reus), but you can certainly argue that he didn't have the guilty intent to hurt Cernak, and rather he made a negligent choice while thinking about other stuff such as "Tampa's top line and the league's top scoring defenceman currently have a 4v3 in front of my net, I need to go play defense." Kassian isn't for sure guilty of murder murder, but he's for sure guilty of manslaughter. You know what I mean?