The issue is actually pretty simple.
One man show? Sole proprietorship with employees? Same answer: the business dies when the principal dies. Period. ANY permissions or authorities, ALL obligations, end as well. Period.
Some things can be done to smooth over the transition- things like 'durable power of attorney,' but essentially the process is: all assets and liabilities are frozen as the 'estate,' and Probate Court decides what to do.
Now, there are various legal practices that will change the question. Incorporating and trusts are two such methods- the principal may die, but the corporation and trust continues to exist, subject to it's charter.
Kin and staff may mean well, but their hands are tied. They have not the authority to spend a nickel, and no contract exists between them and the customers. It's time to re-do the paperwork.
One of the first things that happens is that someone petitions the court to be appointed as 'administrator', or have their claim as 'executor' of the estate recognized. Only then does that person have any right to notify creditors, sign checks, etc.
Rant on a tangent: This stuff is pretty basic. IMO, it is a scandal that anyone graduates High School without a basic understanding of such matters. The schools have a lot to answer for!
