Can a public defender drop your case without informing you?

What is the name of your state? PA

My sister was arrested two Fridays ago while in the car with her boyfriend. They were both charged with posession with intent to sell. She was assigned a public defender who contacted our mother for bail. When informed their was not enough money for bail he suggested a bail reduction hearing for the following
Tuesday. On Tuesday, my mother contacted public defender to find out what was going on. He informed her that he received a call from some one, claiming to be a lawyer and stating that they would be representing my sister. This mystery lawyer never contacted my sister or my mother. Nor did the public defender ever call my sister to say he was no longer representing her. Since then we missed two opportunities for a bail hearing and nothing else has been done. We contacted public defender on Friday to state this he said he would look into the case again. We have not been able to get in touch with public defender since. What do we do now?

hire her an attorney.

If the public defender has been appointed, he cannot just drop the case. The new attorney has to formally substitute in. Your sister must still show up for her court dates.