Firing/Resignation

EDIT: THE FIRM IS GIBSON DUNN. Please do with that information what you will.

Hi all—I just got the unfortunate news today that things are not working out for me at my current firm. For context—I lateraled from another firm and started at a V10 (my current firm) only two months ago. Did not get any initial warning from HR or anything else to indicate this was coming down the line. I was late on one deadline for a Partner who has been on my ass since I first started and we had a chat about it for 10 minutes, but that was the extent of negative feedback I received.

When told things weren’t working out, I was told I’d have website time for four weeks and that they are treating this as a resignation.

I’ve already started working with my recruiter, but am coming here for any and all advice. Particularly, is there any benefit with going along with treating this as a resignation or should I just let them fire me in order to receive unemployment benefits (assuming I am unable to get a new gig in the next four weeks)? I’m in a pretty dark place right now, so appreciate any help from this group. Thanks.