There are many uses of term life benefits for businesses.  Let's look at some common scenarios where this coverage can be vital.

Partnerships and Corporations.

What if the a partner of officer (with ownership) passes away.  This usually has a significant or even fatal impact on the business especially if the person is critical to the functioning and success of that particular company.  There are two ways to try and remedy this with term life.  The first is to have the company be the beneficiary and entity to pay for the coverage.  If the "key person" passes away, the company can use the life benefit to buy his or her shares so the company can continue.  This needs to be spelled out in detail within the structure of the company so this process smoothly transfers.  Back to the question of what to do if a "key person" passes away, this benefit may also be used to hire a competent replacement for the deceased partner/owner.  When companies are formed, rarely do the people creating the company foresee or plan on such an occurrence.  Death is probably the last thing on the minds at essentially the birth of a new entity (the company). 

Family Business (including family business)

The needs for term life insurance in a family business are numerous and maybe even more critical since small business typically rely on the ability and work of one or two individuals.  Family business can rarely manage the loss of a key business person.  The term life benefit can be used for paying off existing debt, floating business such as payroll and inventory in the interim, finding managers or other people to try and maintain the business.  Think of the consequences of losing a key person from a small or family business.  It's a period of tumult aside from the tremendous emotional loss and term life can be used to at least address the financial well-being of the business which for most small business, means the financial well-being of the family itself. 

There are situations (which are quite common) where the key person cannot be replaced.  This might be true for an attorney or builder.  In this case, term life insurance benefit might be used to float the business or put it up for sale.  Businesses are complicated entities and their sales do not occur overnight.  It might be months or more before the transaction can be completed.  Term life will make sure a family does not need to fire-sale a business or present it in a sub-optimum (say debt-laden) condition so as to sell as intended.

Self-Employed

The self-employed share some of the same concerns as the family business mentioned above and business uses of term life mentioned above are equally applicable.  Usually, term life is used by the self-employed much the same way as it would be used by normal personed employed at a company.  It's mainly a way of replacing lost income or paying off debt.  There can be business debts that come into play however and this is where the business use of self-employed can protect a family from such debt.