I’m hoping the landlord will allow us to just pay for the next month while we wait on closing and moving our equipment and inventory over, but I’m curious what they can legally do to make us vacate should they become unhappy with the situation. 

There’s no guarantee that this will help the homeless population, or even if the homeless will willingly accept this and try to make their situation better.

I have a situation here.

In the future just modify your lease to address this situation.

If this is a situation that you are personally facing, go hire a lawyer.

So here’s my situation: I live in Oregon but I invest in the Midwest because of prices in my area.

Even if you plan to self manage, always include the management fees in your analysis so you don't get stuck in a situation where you have to self manage in order for the deal to work.

The absence of a written agreement makes the situation worse. 

In fact, they started telling me about the issues that the girlfriend was having and how bad I should feel for her in the situation, and she is a victim, etc. 

If this credit drop is urgent to recover, I'd be proactive and call the lender/servicer and see what you can do to make this go away.