Our Gemara on Amud Aleph discusses the forms of transgression that the sacrificial goat on Yom Kippur atones for. When the Gemara turns this discussion toward the sin of murder, it wonders what kind of murder sin would require such atonement. If one killed intentionally, he would be subject to punishment. If he killed unintentionally but through negligence, he would be obligated to go into exile. One of the answers the Gemara offers is regarding a person who had committed murder unintentionally by negligence but never became aware that he caused this. Since he has no knowledge of this sin, he cannot do much repentance, and therefore, it is for sins such as this that the goat on Yom Kippur atones.
The Ohr Sameach (Laws of Sanhedrin 17:7) notes that our Gemara only suggested a case where he had committed murder accidentally by negligence and was completely unaware of it. This implies that should he know that he had committed manslaughter, even if there are no witnesses, he would be subject to self-imposed exile. If this were not so, the Gemara could have proposed that the sacrificial goat atones for this as well; therefore, we must conclude there is already a mechanism for atonement via self-imposed exile. This has practical considerations, as perhaps, even if one committed manslaughter through negligence, God forbid, it might be legitimate to impose exile upon oneself to achieve forgiveness.
Shu”t Tzafnas Pa’aneach (215) discusses this as well and says that it hinges upon whether one sees exile as primarily a punishment or an atonement. If it is only a punishment, it must be administered by the Jewish court, and if there are no witnesses, one does not get convicted based on their own admission; two witnesses are always required. However, if its primary function is to achieve atonement, then it may be an obligation even due to self-incrimination.
The Gemara Makkos (10a) discusses divine retribution and justice hinted at in the verses describing accidental death and its liabilities:
It is stated with regard to an unintentional murderer: “And one who did not lie in wait, but God caused it to come to his hand, and I will appoint you a place where he may flee” (Exodus 21:13). Now this is puzzling. Why would God cause one to sin in this manner?
Reish Lakish explains: In this light, the verse “But God caused it to come to his hand” may be understood. With regard to what scenario is the verse speaking? It is with regard to two people who killed a person, where one killed unintentionally while the other killed intentionally.
For this person, there are no witnesses to his action, and for that person, there are no witnesses to his action; therefore, neither received the appropriate punishment of exile and execution, respectively. The Holy One, Blessed be He, summons them to one inn. This person who killed intentionally sits beneath a ladder, and that person who killed unintentionally descends the ladder, and he falls upon him and kills him. There were witnesses to that incident, and therefore, that person who killed intentionally is killed, and that person who killed unintentionally is exiled, each receiving what he deserved.
The simple reading of this Gemara implies that just as justice is not served until the premeditated murderer is executed, justice is not served until the negligent murderer receives exile. This indeed implies that there is an obligation for exile, even when there are no witnesses.
The Maharsha (ibid) raises this question and answers it, indicating a different thought process regarding exile. Maharsha explains that the main function of exile is to protect the murderer from the relative who can avenge the death by retributory killing. The avenging relative is exempt from prosecution if the murderer leaves the confines of the miklat city. Therefore, Maharsha says, even in a case of self-admission, the avenging relative would be allowed to take retribution because the murder was determined to be factual, and therefore, the murderer must go into exile and take shelter in the miklat city.
According to Maharsha, self-confession of negligent manslaughter does not necessarily obligate exile to achieve atonement, but it might still be operative as a necessary social convention to regulate the vengeful instincts of family members.
Notwithstanding the Maharsha’s elaborate explanation, the simple reading of the Gemara indicates that the obligation for exile can be independent of testimony or a decree from the court.
Personally, I do not believe the Gemara in Makkos is problematic for those who would still take the opinion that there is no expectation or requirement for exile based on self-confession. Since it is aggadic in nature, the lesson and allegory imparted take precedence over halakhic precision in the words (see Yerushalmi Chagigah 1:8). Therefore, we might say that the person who was liable for exile but had no witnesses is shorthand for somebody who has a guilt burden of someone who would incur exile if there were witnesses. It doesn’t really mean that he is obligated in exile right now, but it does mean that he has a particular guilt burden that he must expiate. Meanwhile, in this case, the manner in which his punishment and atonement are divinely achieved is by him being sent into exile for the second accidental murder, as per the case described. However, that doesn’t mean there is always the same divinely ordained guilt burden, nor does it imply that it is even recommended to self-impose exile to stave off punishment, because it is not clear at all that he has such an obligation, although, of course, he has some obligation toward repentance and repair.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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Rabbi Simcha Feuerman, Rabbi Simcha Feuerman, LCSW-R, DHL is a psychotherapist who works with high conflict couples and families. He can be reached via email at simchafeuerman@gmail.com