Is it true when a personal pronoun is used as a subject in a sentence it is in the objective case.?

No, it is not true.

When a personal pronoun is used as the subject of a sentence is is a subjective case.

Examples:

Mother made the cake. She bakes often. (the personal pronoun 'she' is the subjective case, subject of the second sentence)

My cousins are coming to visit. They are expected at four. (the personal pronoun 'they' is the subjective case, subject of the second sentence)