They show complete accountability. They dont make excuses. They don't say stupid things like "it just happened". No No No. A sign this person can change is if they are direct without excuses.
They Know Why They Cheated
THIS IS HUGE. They know why they cheated on you and are able to articulate the flaws of the relationship that led to their desire to cheat. If this cheater is telling you about flaws in the relationship and being honest about how a new person rose their level of attraction? It is a HUGE sign that they are honestly reflecting on the relationship, care about the relationship, and are constantly thinking about how to improve the relationship. I am not talking about excuses. Honest reflection communicated to you.
Grey Space in the Relationship
Remember Ross from Friends? “We were on a break!” In other words if they cheat during a grey line in the relationship. It may technically not even be cheating to them.
They Told You Direct
Your partner was blunt and completely open about what happened and didn't try to hide things. If the cheater told you right away. If they were just completely open and blunt and showed you their phone and everything. Then yes. They could change.
It Was a Fantasy
Say you are in a MARRIAGE and it was a one time event. They had sex with a co worker. Or some guy fucks the nanny. If you have a life together and because of depression and a bad marriage they seek to escape with a one time fling. Then yes. They can change because it was just an escape from the pain of the relationship.
You Have a Family
If you are married and have kids and an established life? It is more likely that they will realize that the family means more than the cheating. They will want to repair things with you and fall back in love over time.
Get immediate couples therapy if cheating ever happens. Also, if they cheat on you with an ex? That is grounds for a breakup. A best friend? Breakup.