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The closest Homura is to dying is at dawn, when she comes home after hours of killing witches. She never sleeps - she doesn't need sleep, and her dreams are always nightmares, so she doesn't even try - and is left one on one with her thoughts, and with each passing minute she is closer and closer to blowing herself up.
She remembers every familiar she had to let go, every human she couldn't save, every magical girl that she saw dying or despairing - everything, from every timeline - and the memories won't go away. She bites her lips and her tongue and her fingers until she feels sick from the taste of blood, but doesn't cry, because she's seen what happens to the ones that cry. The despair is already there, and it wouldn't take much for it to swallow her whole - just a couple of tears, one single sob. And she knows - if she despairs, everything will be lost, so she holds it all in and waits for the morning to come.
Then, at school, she sees Madoka, sees the smile that's more precious than her own life could ever be, and just for a moment, there's hope.