When miners are working on two chaintips, only one of them will become part of the longest chain. From the perspective of the longest chaintip, the stale chaintip might as well not exist: the miners expended the effort to mine, but their block reward doesn’t exist in the longest chain.

There are three possible outcomes:

• The soft forking chain gains majority hashrate and wipes out the non-forking chain. In that case, the miners that mined the non-forking chain bet incorrectly and lose their rewards.
• The soft forking chain only garners minority hashrate and falls behind in total work. Miners that mined the soft forking chain expended the effort to create the blocks but didn’t get paid in the main chain. They give up and rejoin the majority chain.
• Neither side wants to give up their rewards, the split is made permanent, and each set of miners gets paid only on their chaintip. Both sides have slower blocks until they reach the next difficulty adjustment, which takes longer for the minority hashrate side, significantly longer if the split is very uneven. If it is almost completely one-sided, mining 2016 blocks at the pre-split difficulty may well be economically unfeasible.

All that to say, whoever ends up on the losing side of reorgs “gives up”/looses revenue.