Thanks for all the replies so far. I'm doing this on my phone so I can't go back and tag specific names, but I'll try to answer questions as I remember them.
If I am understanding the first responder correctly, and the security deposit has to transfer to me upon closing, then it would be in seller's best interest to have her out before we close. She would at least get 850 out of her 2000.
Which leads me to the second responder, and I agree. If the tenant is this far behind, she's not going to be able to pay the seller back (specially if she's about to have to come up with a first, last, security for a new place…). I don't understand her reasoning either, but this is just what our realtor is conveying to us.
I believe the third response asked why she was selling – it is to settle an estate. The original owner had many rental properties, and the daughter has been selling them off.
We actually just found out how far behind the tenant is on rent. All we knew up until this point is that she was sometimes slow to pay. We were planning on terminating her "lease" all along, within a month or two of closing, but with this knowledge, I just want her out before we move in. I don't want to deal with her. And as far as doing damage – she actually seems like a really nice girl – so I really don't think she will do anything. I would just feel better having all my bases covered. This house needs so much work, I doubt there's a much damage she could do that we wouldn't be addressing eventually anyway.
As far as how good the deal is, I think it's a pretty good one. It's a turn of the century house in the Highlands in Louisville, Kentucky, in a great neighborhood. It's fairly large and has an unfinished attic that we are going to finish out to add square footage. With the Carriage house in the back we will have some rent income the whole time we are there. We are purchasing for 280 K, will put 80 K in it, and we will live there for five years-ish. We do 90% of the work ourselves, as my husband is a general contractor. We hope to sell for 450+. This isn't a typical house hack or flip, as far as the BP community goes, but this is how we apparently do things. It's almost like a hobby. My goal is that we could we can to do faster track projects on the side.
We are just finishing our first house, which we did in similar fashion. Once we sell it I'll post the results.
Thanks again everyone!