What if after this phase the first miner or more than 51% of them decide to keep the current production rate ? Do their block will be refused like if they had produced a wrong block ?
Exactly. This is no different than if a miner (or a majority of miners) created blocks which paid out anything more that 12.5 BTC today: the network would simply ignore the new blocks, and the miners will have wasted their resources, working on an invalid block.
@JBaczuk's answer is technically correct that this would create a hard fork, but it ignores the bigger picture that even if a majority of miners make the switch, that doesn't mean users will follow. So while the miners could create a new, hardforked chain, this would be rather uninteresting, as there would be no users on it. As we've seen with past events (ie, blocksize debates, Segwit2x, etc), miners will follow users, not the other way around.
If this were not the case, then users (and the network's rules) would be at the whim of the miners. This would create a broken system of incentives, as miners could just change the rules to benefit themselves (eg, changing the issuance of new coins).
I think that the miner's main motivation for not inflating supply has nothing to do with losing value of their already-mined coins, and everything to do with following the network's users (since they are the source of economy). See: Segwit2X, UASF, etc. If it were possible for miners to increase the supply, I would expect them to do so: inflation erodes the value of every coin in the system, so in some sense this is a situation where 'the losses are socialized, and the profits are privatized', and thus the miner will benefit. – chytrik – 2019-09-06T23:41:36.047
@chytrik it is possible for miners to change the supply and has been since the beginning. I see your point though since the value is determined by the market (users) but many users are miners as well. – JBaczuk – 2019-09-06T23:59:22.743
1'Possible' is a tricky word here, because while it is technically possible to make this change, in reality it is likely almost impossible to accomplish. So I think it is a slightly misleading description, that requires further explanation at least. Looking at the history of the network, there is nothing to indicate that any attempt at this would be successful. So it is possible in the same way that 'adding a tax to every on-chain tx, that pays Chytrik 1% of the amount transacted' is possible, but I'm fairly sure it will be impossible to convince everyone to make that change :( – chytrik – 2019-09-07T00:05:49.667
2@JBaczuk "it is possible for miners to change the supply and has been since the beginning" I couldn't disagree more with that statement. Sure, the entire ecosystem may make that decision (and small but economically relevant groups may be able to convince the entire ecosystem to do so, or split into one that does). But miners are not special in any way in that equation; they are part of the ecosystem, but not more than others. – Pieter Wuille – 2019-09-07T00:22:20.193
@pieter Miners may create the forked chain, but that doesn't guarantee users on the new chain, is that what you mean? – JBaczuk – 2019-09-07T01:04:01.260
2Yes. And underlying PoW's security is the assumption that miners act in a rational fashion (if they're all irrational, PoW does not guarantee convergance). So without users to give the forked chain value, no miner will choose to mine it. – Pieter Wuille – 2019-09-07T01:05:32.807