When Dr. Phil says, "You OWN (fill-in-the-blanks)", what does it really mean?

We all have done things in this life that we are not proud of, and the majority of us have done those things in our teens and early twenties, and I think it is ludicrous for people to hold grudges that are decades old.

What is the person suposed to do with what he/she "owns". The past cannot be changed, and to continue to be punished after so many years is abusive... by the so-called wronged party.

Things seldom happen in a vaccuum. At worst, there has to have been some provocation on another person's part, at best most of such people were too young to deal with things in a more mature or more acceptable way. Most of us are not the same people we were in our teens or 20s, so why should people continue to be punished?

So again, how do you move on when "you own" something and amends are either impossible (because the parties are already dead) or not accepted (because of people's unforgiving and punitive attitude)?

This is a great question. When you 'own' something in this context then amends are due, so to speak. The trickey thing about making amends though is to NOT get tied up in expectations of others' forgiveness, etc. This is incredibly difficult. Amends making involves you embracing full responsibility for the role you played in hurting another.
Of course it is possible to make amends after death; my mother came over from the other side and we both made amends to each other. It was an amazing experience. I utilized a psychic in this instance but my father simply 'visited' me moments after his death. There are no constraints imposed. "The life ends but not the relationship." Amends really consist of you making the appropriate level of sacrifice to the extent that you are convinced you have connected with whatever role you played in inflicting suffering on another. When this authentically happens, you feel remorse, show that to the victim to the best of your ability to convince them of such and in the process, forgive yourself. Whether my past victims forgive me is another matter of course. They may decide they never will and they have that option of course. Can you see how the expectation of forgiveness is simply the antithesis of what amends seek to accomplish? We need to direct our focus and our energy toward a heartfelt "I'm sorry" that is MORE than just words. And do this until we can feel the difference in us. This takes years and years my dear and is a wonderful, worthwhile process. I consider service to others to be a simple extension of the fact that I owe a huge amends to the universe for what I've done while active in my chemical dependency. So in my case it's a lifelong process. I simply love the fact that you are insightful enough to ask this question; it suggests to me that your heart is in the right place.

you own it take responsibility and cake care of the situation