He's said recently that his son-in-law will take over and that he'll be leaving the company "in good hands".
No. Top Rank is a big company and it will remain no matter what happens to Bob. When Arum passes away, someone else will step up.
Seriosly though, his stepson Tedd DuBoef is next in line. He's already really involved in the company and does a lot of the work as Bob gets older.
I'm not sure of who takes over - but I can't see Top Rank just going under when Arum does leave. He's suppose to have a good group around him and he has a nice stable of fighters. I think the company maintains their position and may actually open the door to working better with other promoters. Arum is old and stubborn - sort of stuck in his ways. A new face - with new ideas would probably help not only the company - but the sport as well.