yes it is possible, the psychological /mental health term for this is called ......integration.......each of my DID type alters integrated when their job, purpose, reason for being was no longer there.....example when I was able to handle situations where I would become sad and cry, that alters who's job, purpose, reason for being was to hold those memories and emotions for being sad and crying integrated with me meaning everything they were became what I am today...I now have those memories, emotions, everything that made that alter who and what she was is now me....I now am able to remember traumatic events that lead to my crying, I can now express the emotions of sadness and crying and I am now able to handle present/future events that may result in my needing to cry/express sadness..

here in NY a past self with DID is any alter that holds any emotions, trauma, events, ..from yesterday and before, so by NY standards every alter is a past self alter....the reason for this standard is when a person talks and does things it is done in the past (I had to work yesterday) present (Right now I am enjoying a cup of coffee and internet time during my break) and future (tomorrow I have a very busy schedule)

now if you are talking about a past self as in the religious practices of reincarnation, well here in the USA the DID diagnostics are that this kind of thing has to be ruled out. the problem cant be because of things like living and acting out a past life (common religious beliefs and practices). So to take care of this type of alter you will most likely need the help of your treatment providers who can help unravel why your past life is for lack of better terms "haunting" or "possessing" you.