Is eating 1000 calories a day safe or do you think your body can't survive on that caloric deficit?

Survive, yes. healthy no. It's also not a great way to weight loss if that's what you're going for. At that point, your body begins to work to conserve energy and slows your metabolism down. Assuming you're burning the average 2000 calories a day, just by being alive, 1500 is about the lowest you want to go. For most people, this would set them up at about 2lbs per week.