Suppose Bob gets a typical term life insurance policy and pays the premiums through the contestability period. Bob is then diagnosed with a terminal illness. There are treatments for this illness which have a probability p of keeping Bob alive for the rest of the policy's term. If Bob elects not to receive any such treatments and, as a result, dies of this illness in the policy's term, does the insurer have grounds to deny or reduce the claim? Do those grounds depend on p? Do they depend on whether Bob is unable rather than simply unwilling to undergo treatment? Assume that there are no misrepresentations by Bob and the policy does not specifically cover this situation.
Suppose Bob gets a typical term life insurance policy and pays the premiums through the contestability period. . . . If Bob elects not to receive any such treatments and, as a result, dies of this illness in the policy's term, does the insurer have grounds to deny or reduce the claim?
No. This is not one of the reasons that an insurance company is allowed to refuse to pay a death benefit when an insurance policy has become incontestable. Once premiums have been paid through the contestability period, the only grounds upon which the insurer may deny or reduce the claim are:
Bob isn't actually dead. A life insurance company almost never disputes this issue if it is presented with an apparently authentic death certificate, and it routinely requires claimants to provide it with a death certificate if it doesn't already have one in its file. But, if Bob walked into the insurance company's office alive and well, with his own death certificate, and handed it to the claims adjuster for the insurance company, the insurance company wouldn't write him a check.
After the contestability period expired, Bob stopped paying the premium, was given a warning that the policy would terminate or have a reduced premium if he didn't pay the premium by the end of the grace period for doing so, and he didn't pay the premium. In the case of a term life policy this failure to pay would result in the insurance company having no obligation to pay the benefit. In the case of a whole life policy that has not already had all premiums contemplated by the policy paid in full, failure to pay the premium will usually only reduce the amount of the benefit that is payable by the insurance company upon death relative to what it would have been if the premium had been paid in full.
Bob has transferred the policy to someone else who will be entitled to the benefit instead (e.g. in a viatical settlement or a transfer of the policy to an ex-spouse or trust).
Bob died after the life insurance policy expires for reasons other than non-payment of a premium (usually because the death happens at an age older than the age covered by the policy). For example, my life insurance policy has a provision that states that no life insurance benefit is payable and the policy terminates upon my 75th birthday. This reduces the premium I pay and isn't a concern to me because after I'm that old I won't need to make up for any lost income in order to provide for my children. Another kind of life insurance policy that doesn't always pay a benefit when the insured dies is a "second to die" policy that pays a premium only when both of the insureds (typically a husband and wife who anticipate a large estate tax liability at a second death) have died.
Bob had an accidental death policy rather than a plain vanilla life insurance policy. In this case, Bob's death from a terminal illness would not be considered accidental unless, for example, he actually died because a tornado hit the hospital he was in before he died from his terminal illness. What constitutes an accidental death is sometimes the subject of litigation.
The whole point of an incontestability clause (which typically makes the policy not subject to contest after one to two years) is to prevent life insurance companies from refusing to pay a death benefit in situations including those like the one described in the question.
Generally speaking, state law requires that life insurance policies to be incontestable after one to two years.
An incontestable policy can also generally not be contested on the grounds that misrepresentations were made in the application for the life insurance policy, and preventing refusals to pay benefits in these situations is the other main reason that life insurance policies become incontestable.
Note that even in the case of an accidental death policy, after the incontestability period expires, the life insurance company may not refuse to pay a benefit on the basis of fraud in the life insurance application. Once an accidental death policy is incontestable, the only reason the insurance company may refuse to pay a premium other than the reasons that apply to any other life insurance policy (as described above) is that the death was not accidental. Because it doesn't cover all possible deaths of the insured, accidental death policies are generally very inexpensive relative to the size of the benefit, compared to term life policies covering the same period of time for the same insured.
Also, even if the insurance policy was still contestable, the insurance company could not refuse to pay the death benefit if Bob had been truthful in his insurance application at the time that it was made and Bob had kept his premiums current through the date of his death. For example, if Bob applied for his life insurance policy in January and answered every question on his application truthfully thinking that he was healthy, his application was approved in February, he was diagnosed with a terminal illness in March, and refused treatment and then died in April, the insurance company would not have a right to refuse to pay his death benefit, although in that situation, the insurance company would probably conduct an in depth investigation before agreeing to pay the death benefit.
One of the reasons that the law doesn't allow insurance companies to refuse to pay in these situations is that (1) everyone dies eventually, so dying sooner only modestly adjusts the timing of when the benefit gets paid, and (2) the vast majority of people try to stay alive, even when there will be a death benefit payable when they die, if there is any realistic chance of doing so. Therefore, the economic cost to the insurance company of allowing some people to decline medical treatment when faced with a potentially deadly illness is very modest.
The contestability period only exists at all to prevent people from applying for life insurance policies and lying about their lack of a known terminal illness when they apply for life insurance, which would allow people to avoid paying a life time of premiums and still receiving a life insurance benefit. But, since a terminal illness is pretty much defined as something that is expected to cause you death in six months or less, a year or two of contestability is usually sufficient to prevent this potential loophole from being exploited by unscrupulous terminally ill people.