here is one hypothetical scenario:
1. Bitcoin price (for whatever reason) drops down to 0, that means there is absolutely no demand for Bitcoins, no one wants to pay even $0.00000001 for BTC 1.
2. The number of transactions on the network will reduce, eventually drop to 0
3. Few or no transactions will means there will be no blocks to mine
4. But also, the reward the miners receive for their work (BTC 25 currently) will be worth 0 and as there is no transactions and fees, the reward will be nullified
5. Many miners will stop their machines, only the ones that are mining for the sport of it and their electricity is free will keep mining empty blocks (is this possible?)
6. The difficulty will collapse dramatically, proportional to the hard-core miners hashing power left on the network
7. These few miners will earn(?) Bitcoins at a rate they never dreamed about, but of course these Bitcoins will be worth 0 at that moment
8. Everyone by default will become a hoarder.
9. All hoarders will wait for one of the two things to happen - someone suddenly decides he need Bitcoin and creates demand for Bitcoins or the end-goal of 21,000,000 million Bitcoins is reached and then the network suddenly stops to a halt, as there is no transactions, no fees, no reward, and no reason to waste electricity on.
10. Years later, someone invents a great application for the well forgotten Bitcoin, resurrects the projects, Bitcoin jumps to $zilion level, then everyone frantically starts searching through their grand parent's computers and USB drives for wallet.dat's with the hopes of becoming Bitcoin zilionaires, again...