we bought a triplex in a low income area, and i had met the tenants during inspections - though we told them i was going to manage the place, not own it. they were a little nervous, and i tried to be brief but upbeat with answers.
right after closing and i got the keys, i went over and knocked on each door to introduce myself, short, simple, keep it nice. i took with me a letter stating New Management, my name and contact info, Where/How to pay rent, and stated that we would adhere to all the rules in their one-year leases, which were still in affect. (the tenants were scared we were going to try to move them out or something.) we also brought a form with us to "double check" who was living there, any pets or kids that might not be on the copies of the leases we had, and get their contact phone numbers in case of emergencies.
long story short, within 3 months, everyone had moved out because they decided not to pay the rent. it seems the previous manager had been extremely loose about rents and maintenance. it was a nightmare at the time, but a blessing in disguise! today, we have a nice, clean, repaired property with great tenants that we hand-picked.