Is it true that the closer you get to death the more your body start to curl up into the fetal position?

Dying Process: While this occurs in some people, this stereotype is not the usual situation. One scenario in which this can happen is the frail elderly patient that has a slow decline, confining them in bed over a prolonged period time. Then the large muscles, from disuse, begin to contract and atrophy, and the body becomes curled.

Yes : Because you are loosing bone mass that makes your body like that

Muscle contracture: As the body dies, dehydration combined with malnutrition will cause the large muscles to contract leading a 'fetal position' appearance.