The Drawing
Warning: this section contains spoilers.
The real drawing was drawn (!) by director James Cameron and based on pictures of Kate Winslet.
In the movie, Rose is engaged to Cal. She however is absolutely not satisfied with the life she is living. Her mother, Ruth, is very happy of her upcoming wedding because her husband died, leaving her a lot of debts. Aboard the Titanic, Rose, attempting suicide, meets Jack, whom she ends up falling in love with. She takes him into the suite she is occupying with Cal and he makes the drawing of her, naked, wearing the necklace Cal offered her two days before. They put the drawing and necklace into Cal's safe and leave, as Cal's manservant is arriving.
After learning of the sinking of the ship, Cal finds the drawing and, angry, prepares to tear it up. He then thinks of something else. He makes an arrangement to make sure Jack will not be able to leave the ship. Jack dies, Rose and Cal survive. Rose changes her name to Rose Dawson, Dawson being Jack's last name, and pretends to be third class. Cal looks for her aboard the Carpathia, which has rescued Titanic survivors, but she hides from him. She starts a whole new life, becoming an actress. She gets to marry a man by the name of Calvert. They have children. Calvert dies. Rose lives until over the age of 100. She goes aboard the Keldysh to tell her story to men looking for the Heart of the Ocean, the necklace Cal gave her aboard the Titanic.
All along the movie, we believe that the necklace has sunken with the ship. However, Rose, at the end of the movie, at night, goes secretly to the stern of the Keldysh and throws the necklace into the ocean.