Leaving first base

[shipwreck]

We had this happen last night in a Varsity Fed. game. Girl hits ball to shortstop, who throws to first in time to beat the runner, but first baseman drops the ball. Runner arrives at first clearly after the ball, but doesn't see the ball come out or hear the umpire rule safe. She leaves the base heading back towards home to go back to dugout and gets about 10 feet away and hears the coach holler to get back to base. The ball has already went back to the pitcher in the circle and she throws back to first trying to get the girl out. Two questions 1. Would the girl be liable to be put out in this situation and 2. say the pitcher had not made a play on her and just stood there, would she have been out for failing to keep contact with the base while the pitcher had the ball in her posession in the circle? Dave