This would encourage your loved ones to keep you alive until you reach that age.
In life insurance, you pay the company a small periodic payment in exchange for a large lump sum payment if you die while the coverage is in force. If you die after paying just one premium, you win! If you live so long that you paid more in premium than the lump sum, you lose!
With an annuity, you pay the company a large lump sum in exchange for a small periodic payment for the rest of your life. If you die after receiving just one payment, you lose! If you live so long that the company pays you more than your initial lump sum payment, you win!
https://en.wikipedia.org/wiki/Life_annuity
and
An insurance that pays your loved ones if you die is called a "death insurance".
An insurance that pays you if you live past a certain age is called "life insurance". It's basically a pension fund (except that your loved ones do not get any money you set aside if you die - so usually people take both life and death insurance)
Besides insurance companies for profit motive aside, this might create a lot of unnecessary medical procedures to simply prolong someone's life, even if the quality is total shit.
a) overcharging you for covering the risk of you dying too early (death insurance is marketed as 'life' insurance)
b) overcharging you for covering the risk of you living so long that you run out of money (fixed annuities).
Disclosure: I am the founder of https://tontine.com which will shortly launch a lifetime income solution that will reward you for living longer and we are hiring.
If you are rich and spend say $200K annually on yourself in retirement and buy an annuity that pays $300K annually, and you tell your heirs that the $100K excess will be given to them annually, that would create an incentive for them to keep you alive. If you are that rich, however, they might want you to die sooner to get access to your other assets.
So you pay me (the insurer) a monthly premium and if you live to be 150 years old I pay you a million dollars and if you die earlier than that all I get is the money from the premiums? Ok, I'll take that deal and wouldn't have any problems getting reinsurance on it. Fantastic, write me a check.
150 y.o is a bit too high? Ok, no problem we'll make it 109 years. I'll still take the deal (and your money).
Lower that to you making it 40, 50 or 60 y.o to get the payout? No thanks. Well, not without a full medical and access to some actuarial tables :)
And encourage the insurance company to want you dead.
I like the thought exploration and fear the incentives.
Insurance company: " Pay me $xxx per month, if something happens to you, we will pay you X"
You may benefit i.e your insurance claim is more than the premiums you have paid, or you can loose out by paying more insurance over a time period than the claim. Or simply loose all together where you keep paying and you never get the opportunity to claim.
The insurance company operates like a casino, probability is calculated so it always earns more than it looses.
Think of whether it's worth it from the perspective of the seller to insure only one person? Short answer is no, because that's extremely risky. When you sell insurance policies to thousands or millions of people instead, you can use actuarial statistics and finance the policies with bonds in such a way as to ensure you will make money, with the scale limited only to how many policies you can sell, independent of whether any specific person lives or dies.
So why is life insurance worth it from the purchaser side? Many people will argue it isn't. You're virtually guaranteed to lose money. But the argument in favor is that an early death can be disastrous to others who depend on you and can't support themselves otherwise. It can be worth losing money to gain peace of mind. But really, that is the main argument. It's not a good investment. It's protection from disaster.
The only real analog on the other side is the possibility that a person lives much longer than expected without being able to support themselves, leaving loves ones on the hook. But the best form of "insurance" against that happening is pensions, social safety nets, and the individuals themselves simply saving and investing well as long as they're still working. Whatever money you might have allocated toward reverse life insurance, just allocate toward appreciating assets that will generate income when the person you're reverse insuring stays alive.
https://en.wikipedia.org/wiki/The_Wrong_Box_(novel)
Just like with life insurance, there is some opportunity for abuse...
If your loved ones love you in return that's an incentive for them to keep you alive as long as you are deriving value from life.
If they don't, you might not want them to have an incentive to keep you alive to arbitrary age.
If you die early, the buyer gets the property for the price of the initial down payment which doesn't exceed 30% of the price, if you live for a really long time the monthly payments can easily exceed the price of the property. So effectively, it's a gamble on the lifespan of the seller.
Why would they need external encouragement for that?
For another you could just cut them out of the will if you die young?
I don't know what problem such an insurance could solve.
The best way to insure your kids and loved ones try to keep you alive is to behave in a way that will (hopefully) cause your kids and loved ones to like you.
You may say "that's ridiculous". But how much do you trust the ethics of CEOs of large financial firms?
Why would I want to become that old, if I can't keep myself alive? Why would I want to become a burden to my loved ones?
I'm gathering from the comments that this isn't a globally recognised term, but it's like a flat (or inflation-linked) post-retirement salary based on how much you've paid into it over the years. If you don't get to a pensionable age, you get nothing. Longer you live after that threshold, the more you get paid.
https://en.wikipedia.org/wiki/Endowment_policy
Any insurance product someone is willing to buy exists.
But it pays the insurance company to make sure you die early. :(
Then give your loved ones gifts while you are alive.