No, she stays perfectly safe in District 13. She is not a big part in any of the books, but I take that back, because without her there would be no Mockingjay.
Mockingjay's are first mentioned when Madge gives Katniss the Mockingjay pin.
A gift from her friend, Madge
The mayor's daughter, Madge, gave it to her.
Madge, the mayor's daughter.
When Madge gifts it to her before she goes to the hunger games.
Katniss promises her that she will wear the mockingjay pin durung The Hunger Games.
After the reaping, when Katniss was in the Justice Building, Madge visited her. Earlier, Katniss and Gale sold strawberries to her father and saw Madge, who was dressed for the reaping and wearing the pin.
Madge makes Katniss promise to wear her Mockingjay pin in the arena. This visit makes Katniss wonder if they had been real friends.
She's the friend of Katniss, and gives Katniss the Mockingjay pin.
A mockingjay pin from Madge
In the book The Hunger Games Madge gave Katniss the mockingjay pin because later learned in Catching Fire, Madge's mother's twin sister was a tribute in the Hunger Games and Katniss's mother's best friend. So the pin was given to signal rebellion towards the Capital, and a way to signal Madge as Katniss's friend.
Charles Madge died in 1996.