Hey Robert,
Don't worry. A similar situation happened to me on my first property (a quad too, no less!). It was marketed as "fully rented"...and it was, but prior to closing the following happened:
1st (about 20 days from closing): While reading the appraisal report, I noticed the photos from one of the units looked unoccupied. When I asked the seller, they said they were evicted a few days earlier and that they would make it "rent ready". This was particularly frustrating as this unit needed a ton of renovation and I was not expecting to be in a financial position to deal with that right off the bat.
#2 (about 11 days from closing): I get a call from my agent stating the the seller just received notice that the tenant in unit 4 (who was month to month at that point) just gave their 30 day notice and they would be gone 15 days into me taking ownership of the property.
#3 (AT THE CLOSING TABLE!): After the wire transfer from my bank was complete, the seller tells me at the closing table that the tenant in unit #2 requested to break their lease that morning. I hate to think the worst of people, but I KNOW he purposely waited until the closing agent came in to tell us the wire cleared before telling me.
So, what was supposed to be an exciting time for me instantly became a pressure cooker.
But, like I'm sure you others will reply as well, you are better off to start off fresh with these vacancies as inherited tenants can be a huge pain in the butt. You have no idea what the seller's screening standards were and what kind of tenants you might have been dealing with.
Now you get to do your own screening of tenants - I'm sure you already know this can mitigate so many headaches as a landlord if you screen your tenants well. I know it doesn't seem like it now, but this is a positive thing.
Good luck man, and let us know how everything turns out when the smoke clears. I'm sure you'll be great.