Certainly not an ideal situation, but these are normal investor/landlord problems that happen all the time. Problems create opportunities: Hope (and negotiate) for the best, but plan for the worst.
My first question would be does the tenant have a lease in place? (Hopefully you received and reviewed the leases as part of due diligence). If the lease has time remaining on the term before it expires, and the lease does not have a termination on sale clause, the tenant may actually have a leg to stand on and this becomes a much different situation. In the absence of a terminate on sale clause, the lease normally survives the sale. If the tenant is receiving federal funds such as Section VIII, it gets even more complicated.
If the tenant does not have a lease (or the original lease has expired and/or she is otherwise month to month), and is not receiving any federal funding, then worst case this becomes a holdover eviction after she receives proper notice.
I'm in landlord-friendly Florida, where it's relatively easy to evict someone, and even easier if they are a holdover.
What you need to learn, very quickly, is how long does it take, and how much does it cost, to evict a holdover tenant in Massachusetts? Even though this may be Plan "C", now is the time to look into it and get your ducks in a row and paperwork (lease, notices, etc) lined up. Because the range of possible outcomes here seems to be:
1. The seller and tenant cave, and she vacates prior to closing, maybe with an extension that delays your move in date and renovations.
2. You walk away from the deal and fight with the seller over your EMD. (BTW, for someone to advise this without knowing the specifics of the deal, or your current housing arrangement/expenses, is shortsighted...we simply don't have enough info to make this call.)
3. You get a concession from the seller to cover the cost of the eviction and lost rent, and work though the eviction yourself after closing with a MA attorney.
As scary and terrible as Option 3 sounds right now, it's not the end of the world. In the grand scheme of things it's a small blip in the radar. It's likely a few months' worth of hassle, with the upside of:
-Not losing the deal
-Not risking your EMD
-Not risking your financing & rate lock
-Moving in on time
-Starting your renovations on the vacant unit on time
Even if the eviction takes six months, come Spring, you are are house-hacking a renovated duplex as planned. And you won't even remember the tenant's name 10 years from now.
BTW - What is your other alternative? Renting for a few more years? I obviously don't know - but it's a valid question and something to consider in terms of the overall cost (and opportunity cost) of walking away from the deal.