Welcome serge. I guess for now, what happens between Mary's death and Michael's death is up to you. We all would like to know more and the best way that can be done is by making a GF4 which there is an entire other message board if you wanna discuss that.

However, by seeing how Michael died alone, it shows how different he ended up from his father despite trying to be like him and be strong for the family. Michael always tried to keep the business strong for the family, the people around him he loved very much. In the end tho, he died alone with only a puppy nearby. Vito died happy while playing with his grandson and family around. Kay and Anthony most likely never talked to Michael again and blamed him for Mary's death leaving Michael with basically nothing. It's your choice to believe what it is tho until GF4 comes out if it does.