He clearly didnt grow old a die, because in the modern day we still have Barnes as the Winter Soldier.
Whats DIDNT happen is that Bucky wasnt blown up by Zemo's experimental bomb, because the last issue of Cap has now established that it was Zemo himself who fell victim of that.
That leaves the mystery of how Barnes lost his arm and ended up in the hands of the Russians.
Reality didn't change bucky history. Only caps memories of a world that don't exist. Also inserting characters who never existed.
Zemo has no memories of Steve being his buddy.