The answer to the OP’s question is complex depending upon the type of community. The person who takes solemn vows (eg cloistered nun) does have to decide what to do with all her assets, including businesses, potential inheritances etc and this might mean that she signs them over to a family member or to the community. This is handled legally according to the law of that country. Prior to solemn vows, there are no legal obligations to disperse assets or businesses etc.
Persons who take only simple vows (as opposed to solemn vows) are not barred from inheritances, although these would then become the property of the community as all property is held communally. The vow of poverty is about communal ownership rather than personal ownership, not necessarily about being poor.
My main question would be to wonder why this is even a concern. If someone were going to take final vows, the assumption is that they want to stay in that community for the rest of their life, so naturally they would expect to share all property in community. Prior to final vows this is not even an issue.
If, after final vows, a nun decides to leave the community, they would be provided for in a way that would make it possible for them to start a new life - they are not abandoned to the streets! But they would not necessarily re able to recoup all of their previous assets. That sounds a little like a ‘pre-nup’ – lol.
And I certainly hope no one enters a community with a ‘secret’ business, because that kind of deceit certainly doesn’t indicate much trust in the superior or the community. And it is highly unlikely that the community would want to run a business that was owned by a nun unless it already fit in with their charism and just helped to add income to their already existing source (such as candles or card making etc). They might consider selling it or having the nun sign it over to a member of her family.
If this is a real concern to someone who wants to enter religious life, the thing to do is to discuss it with the bursar or business manager of the community. And be honest about what’s involved in terms of assets and/or businesses. No secrets.