How to handle existing tenants w/o lease agreements when buying?

[Chris Semklo]

Hello,

I'm about to put a offer in on a triplex in Milwaukee, but there is a situation that I'm not sure how to handle. The property is an estate sale which is occupied by family members in each unit without lease agreements. The two out of the three long term tenants want to keep living there. With that said, I'm afraid that if the current residents don't want to sign my lease after I close on the property, I'll have to deal with evicting them at my own expense. Their rent will go up $100 per month because it is seriously under market value. Is there something I can do to reassure myself that I will not get shafted if they decide to reject my rental lease and keep living in the property?   

Thanks in advance!

-Chris