Any system, regardless of the intentions of individuals or the design of the system, is vulnerable to error. Errors happen not only because of venal and dishonest people, but because we are imperfect beings. Well-intentioned people make mistakes.
Any fair system includes procedures to rectify those mistakes, reverse those inevitable errors, and provide some remedy to those who ave been harmed.
While these errors might upend lives and unfairly stigmatize individuals, they can be reversed. Unjust decisions and sanctions can to some extent be undone.
Only one grievous error in a criminal justice system — the execution of an innocent person — is completely irreversible under any circumstances.
No subsequent discovery of a mistake or an error can be reversed after a person is dead.
Of course, a perfect system incapable of error could — at least theoretically — include an irreversible sanction. But such perfection is impossible. Perfect systems do not exist.
Thus, it is impossible to have a death penalty in any imperfect system that sincerely aspires to fairness.