I do believe reconciliation after cheating is possible if the cheating party in question offers up 110% transparency.. no secrets, no lies, no -privacy- to a point, and defined boundaries (cutting off contact with questionable people, for example), for as long as the other person requires it (a reasonable time frame, of course, not "forever")
If the party in question refuses, or if the lies continue, or if a repeat offence occurs? Once a cheater, always a cheater most likely applies, or at the very least, they are not in a mental state that is prepared to handle the responsibilities of being in a healthy relationship (another term for this would be "They need to grow up first")