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It seems that anyone who is familiar with baseball or softball acquires an almost intuitive understanding of a force out or force play. 

Typically, a force out occurs when a runner is forced to advance to the next base by the following runner or batter/runner (due to a fair batted ground ball or fly ball that is not caught) and is tagged out or is put out by a fielder who holds the ball while touching the base toward which the forced runner is advancing.

According to the baseball rule book, even if a runner reaches home plate, no run can be scored if the third out that ends the inning is a force out.

Baseball rules provide a process for the defense to appeal failure of a runner to touch each base to which the runner advances or must advance before the end of the inning.

By rule, for failure to touch a base the advancing runner will be called out if a proper appeal is made by the defensive team.

In the situation described above, application of baseball rules will yield the following result if the defensive team legally appeals the failure of the runner on first base to touch second base during play action initiated by the batter’s hit:

• Since the runner advancing to second base, did not touch second base he is called out upon the defensive team's appeal.
• By definition the out at second base is a force out because the runner at first base was forced to advance on the hit by the batter/runner who must acquire first base.
• The out at second base is also the third out that ends the last inning.
• No run can be scored if the third out of an inning is a force out.
• The inning ends.
• The score remains tied.
• The game advances into extra innings beginning with the visiting team at bat.

This scenario famously occurred on September 23, 1908 during a national league pennant race game between the New York Giants and the Chicago Cubs.

In those days, before electric lighting was available, another inning could not be played due to night fall and a make-up game was scheduled on October 8, 1908. 

The Chicago Cubs won the make-up game.  Obviously, this reversed the outcome of the game on September 23 which would have been won by the New York Giants but for the above described base running error.

Adding salt to the wound of the New York Giants, the make-up game decided the outcome of the national league pennant race in favor of the Chicago Cubs who went on to win the 1908 World Series.