I think you are talking about the first book. She is safe because she could climb well and spend the night in a tree. She was safe enough to get some rest.
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Katniss and Peeta were going to break off the alliance the night the careers came to get them
they did form an alliance but htey did not go in a cave. rue died by marvel's spear when she got coaught in his snare and was reuniting with katniss after she freed her.
. Katniss puts her family first (prim, her mom) and makes sure that they are safe. In the first book when katniss pulled the thing with the gamemakers for her training score she was more concerned about what would happen to her family and if they would be punished for her actions
She told katniss when they were on the woods that the sun glasses that they had were not sun glasses,they were night glasses to see in the complete darkness and at night.
Because the tribute starts a fire in the middle of the night. The flames could attract the Careers or any other blood thirsty tribute