Can a professor fix a mistake in grading after the semester has ended? Let us assume that a professor is handling a course on statistics for undergrads.

They conduct exams and evaluate the answers and award marks to the students. 

Suppose that the professor committed some mistakes, unknowingly, during the evaluation of a student's answers in one of the exams, and as a result, there is an error in the final grade of the student in statistics, and it is not noticed by anyone, including the student. 

If the student realizes the mistake done by the professor in the next semester, then is the professor still responsible for the mistake that was committed? Or is the professor not responsible for their actions since the student was calm throughout the semester? 

If the professor is responsible, then what is the action they need to do if the administration does not allow to edit the grades after freezing them? 

Assume that the professor distributes the answer sheets after their evaluation for clarifying doubts of students regarding her evaluation. And the student can approach them at that time in case of any issues i.e.,  wrong marking.
Yes, the professor is responsible for mistakes she made. Not noticing a mistake doesn't excuse it. But the current situation is no longer under the control of the professor as you state the question. It is up to the administration to correct the error. 

Of course, the professor should make an appeal, along with the student, for an exception to any rule. 

So, in giving an evaluation to the professor you can validly complain about the mistake, but not about the rules made by others. For that, you need to complain elsewhere. 

In general, people are responsible for their own actions and omissions, but not those of others. But they should also work to correct past mistakes however they can. 



The lead question has been edited, so let me add:

While the professor should try to help the student fix any errors that were made, the rules might not allow it. However, I would consider systems with inflexible rules, not permitting errors to be repaired, as unethical. It saves someone a bit of work to forbid such changes, but the accuracy of the record and the fairness to students are values that far outweigh such considerations.