Don't mine until they die, but mine until your electricity costs more than the income from mining. At that point it's cheaper to buy the coins than mining. It's probably not worth it to ship a Jup now anyways.
Mining at a small loss may be useful sometimes. For example it you want to mitigate hash-power concentration. Of course mining at a loss makes more sense with negligible power draw, so I doubt the very large hashers would be able to employ that strategy for long.
With my 1 10 Ghash/s blade, Internet connectivity is the dominant cost. Currently, I have 100% of the mining revenue ear-marked for paying power costs. A faster hasher may pay for it's Internet for a few months: doubt it would pay for the hardware cost though.