Well, we have to remember that the parents have lived at the same address for years

The son knows exactly where to find them if he wants to make up and come home. And that they will give him the warmest of warm welcomes, no questions asked, only insisting that while he is under their roof he abide by their rules, which is fair.
And that every day since heās left, they have been pleading for him to come home, publicly, by every means available to them. He certainly wouldnāt like it if they knocked down his door and forcibly dragged him back to live with them, so they respect his adulthood and donāt resort to force. It doesnāt mean theyāve stopped for a second wanting or seeking for him to come back.
Now assume that heās made clear that he wants nothing whatever to do with them, which is the only situation in which they would act against him, and he has said that he doesnāt consider himself to be their child. Assume further that he has raised his own children and grandchildren in similar hatred, antipathy, and denial of their relationship, since the parents have waited that long in utmost patience, in hopes of his return.
Then they are well within their rights to cut him and them out of their will, to acknowledge his own one-sided rupture of the relationship, his own desire to be no longer part of the family. Which was entirely his choice and not theirs.
Remember also that in doing this they make abundantly clear that on a secondās notice, with the simplest of statements of āIām sorry, forgive meā, and a promise to abide by their rules, they will instantly forgive him and reinstate him to all his birthright.
Even with all of the above - weāre talking about a relationship that goes deeper than a name and a shared address, and that effectively the relationship is a done deal, and was from the second of his birth. They will never and have never stopped being his parents, nor has he ever stopped or will ever stop being their son. Even though they honoured his own free will desire to no longer be considered their child.