If you wonder if your character's children can inherit any successful Startup Business you create in BitLife, the answer is no. In short, BitLife currently does not have the feature that allows users to transfer Startup Businesses over to their descendants. Because of this, if your main/starting character dies, you must use the money your children inherit to start a new business.
We recommend moving to a country that does not have an inheritance or estate tax to increase the amount of money your child gets. Doing so will also allow you to quickly restart your former business with your old character's children. You may also be able to acquire your main character's business using the option called Aquire under the Business Special Career option.
However, this method is not a sure-fire thing as the options for businesses to buy under Aquire tend to be random. Because of this, you may need to reload the game a few times before your old character's business will appear under Aquire. Luckily, you won't need to wait to get your old business back, as the developers plan on releasing a second Business update that will add children Inheriting Businesses in BitLife.
Related: What are Corporate Jobs in BitLife?
When is Inheritance coming to BitLife? (BitLife Update Part 2)
At the time of writing, it is currently unknown when Candywriter will release the second Business update for BitLife. However, we know this update will add the function many players are asking for, allowing children to inherit businesses.
As a side note, another future update for Businesses similar to the Inheritance update will enable users to invest in the stock market. However, this Stock Market update is most likely a separate update from the Inheritance update.
For on BitLife and its many updates, we at Pro Game Guides have you covered with tons of content like Why is my BitLife purchase not working? and How to start a business in BitLife.