Maybe the word you're looking for is:
not capable of being changed or exchanged.
(def. from NOAD)
After reviewing the conversation below, I think I now see more clearly what the O.P. is seeking.
Take, for example, person X who loses a court decision. X can accept his loss, or file an appeal. If the appellate court doesn't rule in X's favor, he can appeal again. But sooner or later, the appeal process ends, maybe because an appellate court refuses to grant a hearing, or maybe because X loses before the Supreme Court. Either way, O.P. is seeking a word that describes such a ruling, the one that essentially says to X, "You have no more appeal options."
It appears to be an elusive term. I Googled
"can appeal court decision" (in quotes), and got back more than a quarter million hits, but when I changed the query to
"can't appeal court decision", I got only five.
I suppose, too, that this generic word need not only apply to court decisions, but might apply to other contexts as well. For example, it could be used in regards to an academic committee that decides to expel a student, or to a controversial decision by a city council. In any case, sooner or later, the person opposed to the decision runs out of appeal options.
If my reformed interpretation is correct, I believe the right word here would be unappealable, which can even be converted to noun form: unappealableness. Collins defines these as:
(law) the condition of not being able to be appealed against
(law) (of a judgment, etc) not capable of being appealed against
Edit to the edit: I actually spent some time researching this, and only noticed Jay's comment above after I wrote all this out! Nice job, Jay; I hope you don't mind my answer down here.