Is returning to first legal?

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One out, man on first. Ground ball to first base, who fields and tags 1st base before BR reaches it. Runner advanced ALL THE WAY to second, but, thinking there were already two outs, steps off second and takes a few steps towards 1st, ( He was not off of 2nd towards 1st enough to have been considered to be abandoning his base), towards his dugout. F3 sees this and throws to second. F4 catches the ball and runs at runner, toward 1st base. Runner catches on to the situation, and backs away from F4, towards 1st base. He winds up in a pickle between 2nd and 1st, and is safe back at 1st. Is this possible?