Can a miner give themselves less than the maximum block subsidy if they wish to do so? The current maximum block subsidy is 12.5 bitcoin. A mined block recently got rejected from full nodes after a miner tried to post the block subsidy as 13.26 bitcoin. But what about in the other direction? Would it have been accepted if the miner posted the coinbase transaction with 10 bitcoin?
Yes, it would have. In fact, this has happened before in many different blocks.

The Bitcoin wiki has two instances of this documented:


  In block 124724, user midnightmagic solo mined a block which caused one less Satoshi to be created than would otherwise have come into existence. Therefore, all calculations from this block onwards must now, to be accurate, include this underpay in total Bitcoins in existence. Then, in an act of sheer stupidity, a more recent miner who failed to implement RSK properly destroyed an entire block reward of 12.5 XBT in block 501726.