Yes, not eating is often a sign of checking out.
My husband's refusal was physical discomfort, he wanted to eat but couldn't. In his later stages when his mental alertness was gone, he'd often make unusual arm movements to his mouth. It wasn't until he was gone that we realized that what we had seen was the movement of him trying to feed himself.

My father-in-law had to be put in a nursing home in his later days. We didn't expect it to be final but expected to bring him home when he recovered from a hospitalization stay. I don't think he believed that he'd ever get to leave and he started not eating. He suffered from mild dementia so our promising he would not remain there went unheeded. We'd bring him his favorite ice cream that initially would be eaten but eventually when anything was offered, he'd pull his blanket over his mouth. There was no physical reason..it was a choice.