Bitcoin's worth or any other cryptocurrency can successfully drop from a relatively high value to zero value.
When the price of a Bitcoin falls below the cost of mining, people will have no reason for mining, and consequently, its value will drop significantly.
Without mining, then there will be no public ledger recording and verifying the Bitcoin transactions on who is now owning the crypto. Then it will become worthless.
The cost of mining Bitcoin is not fixed. As its price increases, new investors enter the market with the aim if mining it. By this, the effort needed to mine the Bitcoin will increase since the profits it will yield will be distributed among many people.
When the price falls, a good number of minors will exit this field hence decreasing the cost of mining it. A low price for the Bitcoin quickly reduces its value to zero.
If its price continues to fall, mining Bitcoins will become absurd. And since people will leave the market, fewer people will be there to verify and record the transactions taking place. Bitcoin will, therefore, become worthless.