This is not a proposal of forking network!
By timestamping first wallet transaction with real time date/hour/seconds into ledger history, bitcoin core software nodes can make an agreement that if, for example:
during the next 2 years the wallet's public address that was timestamped do not output any Tx, bitcoin nodes take those funds and place them into next block header.
If a public address will make a new output tx with any amount of tokens will be re-stamped with date that was realized the last tx.
If the public address won't put a minimum of 1 transaction in 2 years, those funds from public address will be moved into next block of transactions.
I know it sounds easy. But to translate into coding, it is very hard to accomplish.
In bitcoin is harder to be implemented due to multi-sig public keys .
I cannot see another solution to this problem, which can become very important in far future.
I would call this process (Proof of owner's wallet)
As interesting as it may be to bring lost coins back into circulation, there is no real way to proof that the key for an address has been lost.
Two years are way too short; for example, I have coins in cold storage which are much older, and I don't plan to move them in the next two years.
Also, what happens in case you are unable to access your funds just because you can't? Imagine you have a really bad accident and are in coma for two years: you wake up and all your money is gone.
If you want to keep using the age of coins, better consider something like 100 years instead. However, even that might be a very bad idea: assume there is an address with 100BTC which is really lost. Based on your proposal, in 100 years those 100BTC would come back into circulation and some miner would be very happy; but, at that point the network most likely has gone to a level where single Satoshis are the normal amount and worth maybe $1-$10 each. Now you drop 100BTC what will crash the price and effectively make all BTC users have less.
If there is a point where Satoshis are getting too expensive, the better idea is to just add more decimals and create eg Minitoshis, Microtoshis or Nanotoshis.