Would it be possible to create a soft-fork for reducing miner reward? Context:

There is a bet going on r/bitcoin about the possibility of doing a user activated soft fork for reducing current miner reward to 0.25 BTC.

One of the users says the bet had two points:


the change must be a soft fork (aka it doesn't break consensus)
no miner must be able to claim more than 0.25 btc.


Would it be able to make a change to the Bitcoin consensus rules that would meet this criteria?
Yes, it is possible. The rule regarding the coinbase reward is that a miner cannot take more than the block subsidy plus the transaction fees in the block. This means that a miner can opt to take less than the full reward that they are entitled to. This has happened before in Bitcoin a few times. The coins that they did not collect are gone forever.

So, you can use this rule to your advantage if you want to decrease the block subsidy via a soft fork. In your soft fork, you simply create a new rule which results in the coinbase reward being less than the current coinbase reward (e.g. the block subsidy is smaller). Because of the rule mentioned earlier, non-upgraded nodes will still accept blocks that have these coinbase transactions with a smaller coinbase reward. Thus this is a soft fork because the new rule is backwards compatible.