PE recruiting after being fired - story

Hey guys,

I have recently been made redundant and I was wondering how should I deliver it to headhunters and PE funds. I don't know if people have any understanding to this, or whether you are automatically put in the bottom of the list of the headhunters and whether PE funds would refuse to interview you at all?

Should I rather come up with some sort of a story and position it as if I've rsigned for example?

Also, what kind of check do PE firms do upon receiving on affer - can they verify your bonus, ranking, date when you left, etc.?

Thanks a lot!