Negotiating the seller down on sale price from $200,000 - $185,000 to build some instant equity in the property.

And this is CRE, so it's cutthroat, it's no one's problem but your own if you lose an earnest money deposit. 

Which is why there is more investment in real estate and bank deposits  in the “western world” (which includes.

Others will collect first, last, and a smaller deposit.

If a buyer is coming down with a high-down payment and quickly making a large deposit into escrow fighting tooth and nail about proof of funds may be a red herring.Credibility is also a factor here.

So the total amount that should be paid will be rent for remaining days in month + security depositORrent for remaining days in month + next month + deposit - I don't know when would this situation arise.

I'll reach out to the lawyer in the meantime, but I suspect if they refuse to pay it, it'll have to come out of their security deposits when they move out?

At a bare minimum, I would require a written lease agreement and a standard security deposit equal to an entire month of rent.

Your downpayment would be instant equity and your consistent cash flow would lead to equity over time.

Ideally, you'll want to see average 90% occupancy across the board, otherwise you'll be relegated to regional bank and credit union lenders that require (i) recourse, (ii) deposit requirements at close, (iii) slightly higher rates, (iv) lower amortization, and (v) less interest only [if cash flow is a priority for you].