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Their deaths were probably extremely painful and slow.
The first few days would be them talking about what to do from there. Towards the end of the first week the hunger becomes unbearable and they lose the energy to do anything worthwhile. Chii's physically weaker than Yuu, so she probably would be the first to die; By the latter half of the 2nd week, she'd probably ask Yuu to kill her quickly so she doesn't feel more pain from the crippling hunger, Yuu would cry but there really wouldn't be any hesitation. They'd probably use a rag torn from their clothes to suffocate her.
After a few more days of Yuu huddled nearby Chii's frozen corpse, Yuu would probably begin to eat the body (which is surprisingly well preserved, but that's because of how cold it is) to stay alive which would at least last Yuu a few more weeks, but she's only fooling herself because death is inevitable.
Yuu kills herself by the 3rd week after realizing how emotionally dependent she is on Chii.
