Yes, it is possible in some instances although more often that not the signature of the insured person is required. While this always sounds a bit sinister it is not of course, we often are contacted by family wanting to arrange cover for their parents (usually) who would not be interested at all in having or paying, or because of health reasons.
Other than Power of Attorney situations, typically with any form of insurance the person being insured must sign a declaration, therefore by default they are aware of the cover even if they are not arranging it themselves. There is one funeral insurance provider in NZ who we are aware of that will allow a close family member to apply for cover without any knowledge of the person. But that funeral plan is only available for those aged up to 70. The person arranging the cover is shown as the policy owner and typically it must be a spouse, son or daughter of the person being insured. They can also be the beneficiary for the claim proceeds and also be the person who makes the premiums payments.
This options is not just for the more reluctant parent it is also good for a family member who is ill and cannot understand sufficiently to sign themselves. It also avoids all the complications of applying using a Power of Attorney.