Let a being be arbitrary, suppose that this being has the capacity to be morally responsible.
(EDIT 2) Regardless of group morality, but assume this being is in a moral environment with no moral contradictions (at least a priori).
(EDIT 3) I want to clarify that a morally responsible being is not necessarily the whole of an identifiable being (like a human body), this being can be anything to which one can assign moral responsibility, such as our individual ethics or morality (which can fill the moral of its environment), the soul, character or spirit, mind or reason, our genetic code or our functioning as an organism, etc... All these are beings that one could identify as parts of another being, and if you want you can assign them moral responsibility.
Using the principle of the excluded middle we can infer that either this being is mutable or not mutable (immutable).
(EDTT 2) immutable in the sense that at least it doesn't have the ability to change voluntarily (EDIT 5) or in the worst case that it cannot change at all and therefore remains eternal (like god, universe or nature).
(EDIT 6) In the second and worst case of the immutable being we can think of it as a universal.
If this being is immutable, then it could be identified, but how could moral responsibility work in a being that will never change?
If this being is mutable, then it could change its behavior, but how could moral responsibility work in a being that cannot be identified?
Because this being at the moment of mutating is not the same being (being the mutation as radical as you want).
I mean, how could a mutable being be if it never is?
I am not questioning the usefulness of moral responsibility (I believe in its usefulness).
I am assuming that both the mutable and the immutable being have the capacity to be morally responsible (it could be one of these contradictory or not).
My doubt lies in the possibility of making moral responsibility work consistently.
EDIT 1: As Mary said, a mutable being does not necessarily change after being identified, this case seems consistent with moral responsibility.
EDIT 7: I think it is consistent in that case because in simple terms moral responsibility, at least as I understand it, is about identifying a being and attributing good or bad actions to it, if a mutable being can remain unchanged for an interval of time, then it could be identified and therefore eliminate that being if necessary, an example: a child who steals a candy, we could suppose that in some interval of time that child can be identified, once identified he can be punished to correct his behavior, Once this is done, the child that was will no longer be, but moral responsibility will have fulfilled its function.
EDIT 4: I think that with that answer the consistency of moral responsibility in mutable beings is resolved, but the question still persists as to how morally responsible immutable beings could be consistent in the sense that one could not change its intrinsic properties. Or is the assumption of a morally responsible immutable being absurd?
EDIT 8: If it is absurd that an immutable being is morally responsible, it must be that only mutable beings are morally responsible. But there is still a problem to be solved, the sorites paradox about being-identity.
EDIT 9: Probably the last edition, my doubt has already been clarified and I thank everyone who contributed with their answer, I will leave useful links for those who have come up with similar doubts to mine.
sorry for so many edits
I found this SEP entry very related to this question: Personal Identity and Ethics