The stability, or soundness, of a life insurance company can be very important. Life insurance policies are purchased with the understanding that it will be a long term contract lasting for 20 years or more. The financial stability of the company is essential in deciding on a safe company for such a long term investment. After all, choosing a company that goes under would mean a loss of your investment and having to purchase the policy all over again, at higher premiums, from another company.
You can check the financial soundness of a company by using a site such as the A.M. Best Company. The A.M. Best Company has a long history of rating insurance companies and other financial institutions, and provides a simple scoring formula that ranges from A++ downward. Additionally, the AM Best Company looks at both current indicators and the long term financial outlook, giving you more insight into the company you are considering.
When using financial ratings, focus on companies that are ranked in the top 2 or 3 categories. For A.M. Best, that would be companies ranked A++, A+, or A. Lower ranking companies may not have the financial wherewithal to survive a long term contract. The lower rated company may offer better rates, and they might be around for a hundred years, but the question is whether your family's financial security is worth gambling on with the hope of saving a few dollars.
You may find that some companies are not rated. This does not mean that you are dealing with a bad company; it only means that, for whatever reason, the company has not yet been rated. One example might be a company that is a subsidiary of a larger company, in which case the larger company may be rated by the smaller one is thought to carry the same rating rather than receiving an individual one.