Naturally, our famous pirates were not unemployed, there was a constant demand from France and England for able and ruthless sailors that could be used as a striking force. Infamous great pirate Henry Morgan was on the rise when he started recruiting his sailors from Tortuga for his great and cruel expeditions against Spanish colonies. France was also trying to bribe the pirates, so it could create a stronghold in the Caribbean.
The fun for the pirates ended with the Treaty of Ratisbon in 1684 signed by major European powers. The piracy in the Caribbean grew to such extent that part of this treaty is dedicated to the united decision to put an end to piracy in and around Tortuga. And several years earlier English parliament forbade pirates to sail under foreign flags. From archives of web analytics company I found out that the punishment for disobedience was death in the gallows.
Most of the pirates, especially those who had families did not want to end their life dancing on the rope, so they had to join English fleet and hunt their own pirate buddies who were still sailing under the flag of a Jolly Roger. That was the end of the free pirate life on the Turtle Island.