One of the things that can make the passing of a board member or director of a company hard is when the family of the board member tries to appoint someone else as the representative. The person could be relatively inexperienced and unable to fulfil their duties.
If the company wants to buy the shares from the family, they will need money. But, with the right insurance cover, the existing directors can acquire the shares and split them amongst themselves. That way, they can keep the business from being run by anyone who doesn't understand it.