The coin would be like this:
There is no upper coin limit, unlike most coins.
Every X * 25 seconds, the system give (X) coins to a miner.
Every (X / 31540000) seconds, the person lose (X / 31540000) coins.
Explanation
At the movie you need 25 years to get 1 year worth of money (1 / 25 = 25), thats why wait X *25 seconds you receive (X) coins.
Every (X / 31540000) seconds, the person lose (X / 31540000) coins, to represent someone losing one coin second each time second.
Now thinking about it my idea assumes that each 25 years, just one person become adult, and that was obviously not the case at the movie. You would need to change X
Interesting idea, mate. This would well fit into a new cryptocurrency, whose purpose would be for time issuance that will help determine pay rate, life expectancy, among other things. It would be very surprising if this becomes used at a point where it could determine your lifespan (like in the movie). Perhaps, a cryptocurrency with above characteristics using blockchain technology to track every people would become ideal for it.
Nevertheless, something similar like this could implemented for Bitcoin, but in the sense where you could see your current holdings, as well as BTC's network stats. The possibilities are endless, but it would be up to mainstream acceptance from everyday people. Just my thoughts.