So I am going to the local PD and filling out a property check application and installing security cameras on the property.

It is not secured by the business, which is a very specialized franchise (no guarantee a foreclosing entity would be approved as a franchisee by the franchisor, among other complications).

In all my years working as a trustee I never found what one would consider a conventional lender that would lend on an irrevocable trust (I assume this trust is for estate/Medicaid planning).I suppose anything's possible in the world of private lending, but the rates will probably be much higher than conventional.Which begs the question, "why the trust in the first place"?

I have a 2 unit under contract, the current owner told me tonight that the current tenants are month to month, but never signed a lease or gave security deposits.

I think long term we are way less volatile than some California markets (as seen in the last downturn) so there is some sense of security holding through whatever is to come - in my opinion.     

Second, with you living there to determine if you can afford the remaining expense amount with your current income.As far as the private mortgage insurance (PMI) it is required if you have less than 20% equity in the property.  

Does anyone have a suggestion on what I should do to secure long-term financing?

The current tenants did pay her a Security Deposit of $600 and last month's rent of $600.  

Do I draft up a sub-lease and have them have a security deposit and what not just like any other rentals?

You may also try Steve Snyder a private lender.