Doesn't matter. Once you take your vows of the Night's Watch, you release all claims to titles and inheritances. Even if he is alive he is a crow for life. Everyone has turned on him, even his former family, and now his brothers of the Night's Watch. He is going to be bitter after everything he has done for them, even giving up his true love to protect them.
None of that matter though, because he is dead and will be resurrected or healed by the White Walkers with full consciousness, become their leader, and storm Westeros on the back of an ice dragon freezing all of Westeros, because he is the only one in the north who has the ability through blood to tame dragons.
Dany, Tyrion, and.... I don't know, maybe Aegon, are going to return on fire breathing dragons and there will be a battle of the centuries between the remaining survivors who have all but killed themselves trying to gain the Iron Throne, The Hound's fire sword, and the fire breathing dragons whoopin ass against John Snow who is now the villain leading the wights and White Walkers.
And again, you're on crack
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