I already asked the bank if it could be delivered vacant but from how they responded I think they want to avoid that headache.

Have your attorney make it a condition of the contract that the seller deliver one unit empty for you to be able to occupy.

The actual rehab cost was $125,000, and we have delivered the property on time.

Hypothetically speaking, I get a property this way, and it's worth 50k, do I have instant equity that I could use for repairs? 

I've talked to the current PM, and while he's usually leery about managing non-conforming properties, he said the fact that the postal service didn't raise a red flag and is delivering to all four units is good enough for him that there'll be no issues with the county. 

Needless to say I was in shock, and instantly took them that much more seriously.

Recently I've tried sending a certified letter (containing all my contact info and a request for contact) with return receipt, but USPS reports they were unable to deliver it  - Notice Left (No Authorized Recipient Available)There is nothing particularly wrong, and she's completely current with rent based on auto-payments.I feel uncomfortable not being able to reach her.

I found it on ARMLS ( I am a Realtor) and instantly knew that if I turned this unit that it could be a homerun.

The property delivers an 8-10% annual cash on cash return and has ridden the recent market upswing and appreciated about 25-30% in value since purchase (March 2016). 

We still purchased in our name, but we got instant equity by buying a $75k house for $50k.