It is estimated that about 4 million of the about 16.4 Bitcoins ever mined are lost forever because no one knows the private keys of some Bitcoin addresses. This effectively mean there are actually only 14.4 million Bitcoins in circulation even though 16.4 million are mined. There is no way of eliminating the human errors that cause these losses of Bitcoin from circulation, while the number of Bitcoin that will ever be mined is capped at 21 million. This means the total number of Bitcoins that are in circulation will eventually become zero, bringing the network to an end.
The solution this BIP proposes is to implementing a dead man's switch to Bitcoin addresses. The dead man's switch causes the Bitcoins assigned to dormant addresses to automatically expire. A Bitcoin address is deemed dormant if it is not used in transactions for some fixed length of time, say ten years.
The calculation of the miner's reward should take into account the Bitcoins that has expired. This means there is a possibility that miner's reward can increase if sufficient number of Bitcoins expire.
Ref:
http://fortune.com/2017/11/25/
lost-bitcoins/
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