If a kicker/runner safely overruns first base, and the ball is then overthrown, how far may that kicker/runner advance?

Overrunning first base is NOT equivalent to “running toward” second base (see Rule 10.07b), and therefore the kicker/runner would be limited to second base. The kicker/runner is permitted to attempt an advance to third base only if the kicker/runner had started an active attempt to reach second base (see Rule 10.06) before the ball was overthrown.