The system will reach equilibrium when the revenue generated by mining is equal to the amount spent on mining. When the value of BTC goes down, mining generates proportionally less revenue (if miners are valuing BTC at market price, which they may not be), and the global hash rate will drop.
Imagine if the price plummeted, the hash rate dropped, and someone launched an attack on the network. At that point, consumer confidence in Bitcoin would possibly never recover, and its long-term viability would be severely damaged.