Miners will not "mine more at the same expense". They will mine the same thing at less expense.
Individually a miner will mine more at the same expense ( a drop in hashrate that leads to a drop in difficulty means your individual share of the overall hashrate increases, hence you are more likely to find a block. In terms of pooled mining it effectively means you see a higher income in btc paid out by the pool for your provided hashrate).
Overall however (all of them combined) miners will use less resources to produce the same amount of blocks (given that the hashrate then goes into a stable state where difficulty does not change).
Your statement is only true if you regard the entire network of miners.
It does not make sense if you think about it. If 10 people share the production of something equally everyone gets 1/10th.
If 2 leave (drop in difficulty due to drop in hashrate) the product is shared between 8 and not 10.
If the amount produced stays the same regardless of how many are contributing (this is where bitcoin uses difficulty to adjust that production) the remaining 8 will get a larger share.
Obviously if leaving also means stopping your input of resources so overall the production cost sinks by the amount of resources you stopped supplying.