Incredibly unlikely but...
They could use the Chrono Trigger method. Travel back in time and replace the person you want to save with a copy in the instant before they die. Then return with the person to your proper time.
This way you sidestep the grandfather paradox (If you killed your grandfather, you'd cease to exist, then who killed your grandfather). In this case, at the end of the day, as far as you are/were concerned the person still died in the past and you had the reason to travel back and save them.
They could use the Chrono Trigger method. Travel back in time and replace the person you want to save with a copy in the instant before they die. Then return with the person to your proper time.
This way you sidestep the grandfather paradox (If you killed your grandfather, you'd cease to exist, then who killed your grandfather). In this case, at the end of the day, as far as you are/were concerned the person still died in the past and you had the reason to travel back and save them.
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