Bankruptcy. If the market-clearing rent for an area drops below what the developer needs to pay the interest on the construction costs, it doesn't just sit idle (if it does, the developer just goes bankrupt faster). Rather, the developer goes bankrupt, he and the bank both take a haircut, and the property gets sold to a new owner at whatever price the new market-clearing rent can support. The new owner then makes a profit renting at reduced market rates.

This happens periodically in the Bay Area - it happened on a large scale in both 2001 and 2009. It's the best time both to make a real estate investment (folks who bought housing in 2010 are sitting pretty now; I'm kicking myself for not) and to be a renter (I rented a lovely apartment for $1400/month for 3 years in 09-11 that had gone for > $2000 in 2007, and is at about $2800 now).

It's not necessary to pay for construction costs. That's what bankruptcy is for. Of course developers and banks avoid that as best as possible, but there is nothing stopping price from dropping below the cost of construction. It has happened countless times before and it will happen again.

Factories want to get paid for producing product, mines digging gold or ore out of the ground want to get paid as well. But, similar to excesses in housing in distressed areas, circa 2008 (maybe Las Vegas?), someone, somewhere lost money, because price is not dependant on the cost of producing the thing. 'Cost plus' pricing strategy is one of many; cost is not the only driver, regardless of the good.