I guess it could go one of two ways, and ultimately boils down to whether or not the employee has access to the bank account.
Assuming they do, and assuming it's an actual business (llc or whatever) then the employee could keep it going in the medium term, basically preserving the value of the shares.
Once an executor has been assigned, the employee can liase with them about business decisions, appoitment as a formal business decision maker, and so on.
Ultimately the shares will go somewhere, perhaps to an heir, perhaps to the state.
If some compensation is still due to the employee, then perhaps they could get control of the shares - every case would be treated on merit.
If the employee does not have access to the bank account, then the business is basically dead. Without access to cash, without access to revenue, it'll likely fold immediately - probably before an executor can be appointed, and can arrange access to the account.
That said, each case is different and YMMV, especially given the very limited amount of information in your question.
