Considering characters often experience a high turnover rate.  Would it be possible to consider the ability to create a will for each character?  Granted, the creation of the will could come with a fee, but it may help keep things moving if a player puts a ton of work into a business or something like that.

I would be quite happy to allow the descendant of a deceased character claim ownership 'officially' of any businesses run by their parent within a few days or a week of their new account setting up, but I wouldn't want them to be able to hand on BGs, Drugs or cash that they had when they died.