These types of tenants often do this because they don't want to save in advance, so they take the rent owed to you and use it to put down on their next home.Recommend you do a better job of communicating to the tenants that you will pursue every legal collection option if they don't pay last month's rent.Also, why are tenants NOT staying with you?

You need to identify your starting point to determine your options.  

Let me know if you need some good options here; we work with quality accountants all around the country.   

If they don't - then it's optional.  

Most tax software has an option to specify that rental income is non-passive, and that's how you do it.

I might do a deal where I purchased the property and provided the “buyer” worth an option to buy for the period of the loan with monthly rent” payments equal to the interest payments on the would be note.  

However, those two options are too pricey for me.

The art is to increase the rent without running off GOOD tenants (very important, if the tenants aren't ideal tenants then non-renewing becomes the default option).

Are there options for assuming the existing mortgage and financing the remaining balance with another mortgage?

Current lien holder is going to be pretty much your only option.