In bridge, what happens if a bidder makes a wrong bid that can't be corrected?
The Laws of Contract Bridge's Law 36 deals with inadmissible doubles. If the player in first seat takes a call before somebody realizes that the double was inadmissible, the double and all subsequent calls are cancelled, it becomes fourth seat's turn to call, and everything proceeds as normal.

If, on the other hand, the irregularity is called out immediately, the double is cancelled and the player may substitute any call. Their partner (in second seat) is forced to pass every time they make a call for the rest of the auction. In addition, there will be lead restrictions:


  Declarer may prohibit offender’s partner from leading any one suit at his first turn to lead, including the opening lead, such
  prohibition to continue for as long as offender’s partner retains the lead.