Anyone dangerous to the society member (s) should be punished.
Insanity can be faked so answer is not easy. All I can say, the balance should be in favor of society rather than this one person. The fact that the person is a serial killer should be enough for this person to be completely isolated from the society whatever method that may be.
Forever/permanent institutionalization regardless if this person shows ‘cure’ in future is one method.
Moreover, this will deter others thinking of using this excuse to get freedom from being punished.