Well, the problem as I see it is, I just gave my 2 weeks notice when I accepted your offer. I might have even given it earlier and pushed the start date a week forward so I could get a nice gap week to decompress between jobs.

Now, at this new company I've been excited to work for, I receive an email telling me that I in fact do not have a job next week and I am actually unemployed.

My options range from extremely bad (begging for old job back) to mildly embarrassing (attempting to re-accept a previously declined counter offer).

Sure, if you're fired you get unemployment.