Lifespans of people today, especially in the Western world, are longer than they have ever been, and naturally this means that life insurance companies have had to expand their insurance policy offerings to accommodate this new reality. Whereas 40 years ago it would not have made a lot of business sense to offer term life insurance, with its relatively low premiums, to people over the age of 50 who would have a fairly high probability of passing away within the span of 20 or 30 year term life policy. In those days a person in their 50s would've been much more likely to have been routed by an insurance agent into some form of permanent life insurance, such as whole life. The cash value amount that permanent life insurance policies accumulate over time meant that insurance companies could protect themselves from the relatively likely prospect of paying out death benefits at some point in the life of the policy, to a newly insured person in their 50s.
Today an agent would still be quite happy to sell you whole life or another flavor of permanent life insurance, but the fact is that is much easier to buy a term life policy for yourself today if you're over 50. It is simply a response to the fact of average life expectancies in our society increasing: if you buy a 30 year term life policy at the age of 50 for instance, the insurance company is much less likely to be faced with a payout, simply because you're much more likely today to live past the age of 80.
The reason I'm emphasizing the greater availability of term life insurance to older people in this article is because these policies are often a better choice for older policyholders. Often permanent policies sold to older people have no cash value amount for one thing, and the cash value amount is a major reason why people pay the higher premiums for permanent life insurance in the first place. (Remember that you can usually borrow against the cash value amount associated with your policy, or even take it as a lump sum if your circumstances change and you decide to end your policy early.)
While a term life policy will also not have a cash value amount, at least the premiums will be much, much lower than most permanent policies. This frees up cash for one to put towards living expenses or their retirement investment portfolio. If you're over 50 in looking into life insurance options, look carefully at term life policies with provisions that enable you to extend the length of the term of the policy if you're still alive at the end of the initial term. You should also be aware of return-of-premium term policies, which enable you to get back premiums that you paid into the policy. You'll pay more for these provisions but they may very well be worth it.