I have to say that I was never in such a situation. I witnessed a few such cases though in different work environments. Each case was pretty specific, yet some general patterns were there. Here is Rosalia’s case: a young professional who was given responsibility beyond her experience, with the “bonus” of her work friendship at test.
Rosalia was booming when, upon return from a long vacation, she took over the project’s files. She found out that she will be given this project two months ago. Her best friend and colleague, Michael, left for another job in another country. Rosalia was very enthusiastic at first. She idealised her friend and everything he did so her usually active critical sense was put to sleep. Two months later she paid dearly with her health. Her joy soon turned into a depression fueled by a stream of difficulties. A surprise kept popping up after another. A consultant was paid for a product of unacceptable quality. A statutory evaluation was skipped with no explanations in the file. There were no contacts established with the project donor and the project was on its final stage. Large amounts of budget remained unpaid and the budget lines were guarded rigidly by the sponsor.
Could at least some of these have been prevented by knowing what to expect and preparing to act? A proper hand-over, to start with, would have given Rosalia a clear status quo. She did not want to ask her friend any questions of fear to be perceived as challenging his authority. If you find yourself in such a situation, there a few strategies which you could try.
First, ask for a tri-lateral meeting with the departing project manager and your supervisor. It can be over coffee or another less formal set-up. Follow-up the meeting with a note and send it to both to get confirmation on what you were told. It will give you a baseline and your friend will not feel as reporting to you.
Time permitting, organise a joint introductory meeting / a conference call (in case of teams located in different places), where both you and the departing project manager could participate. Follow the meeting with minutes circulated to all concerned.
Agree with your departing predecessor for how long and on what you estimate to still be needing to get back to him/her with questions you might have.
While friendships come in different forms and many complexities might arise, some of the above might allow to set the boundaries between personal and professional relations so that you can continue your friendship unaffected, to the extent you can. Sometimes you’ll have to choose. Sometimes you’ll have to compromise. It’s important not to compromise your professionalism though. A true friend will not ask you this.