Can you accidentally die of starvation?
No you can't. You will get noticeably thinner, noticeably weaker, and noticeably paler. And key here is noticeably. You and those around you will notice it. But, a big BUT, you'll not starve in only a week. Depending on your basic health, it should take several weeks, even a month or two, before starving to death. The thing that can do you in much quicker is the lack of water. The human body can do without fresh water for only a few days.