Throwing Glove Off

Question
This was a High School game...this happened just after the centerfielder has fallen down after a catch: The second baseman is making a play on the runner coming in from first base. The second baseman sees that her centerfielder is down, she throws her glove to the (to help check on the centerfielder) but the shortstop throws the ball to the second baseman. The second baseman catches the ball in her bare hands (glove is on the ground) and tags the runner. Is the runner out since the second baseman intentionally threw off her glove? Should time have been called immediately by the umpire since the centerfielder is down to stop all plays? All of this happened within seconds each other.

Answer
First, there is no reason to stop play because a player removes her glove.  Nothing in the rules prevents something like this.  

The runner is out as long as a legal tag was made.  If the runner was tagged with the ball held in the bare hand, no problem.

In an injury situation, the umpire has the option of letting the play finish before calling time and allowing the injured player to be tended to.  Most injuries would be treated this way.     For most situations/injuries a few seconds doesn't make any difference.  The umpire should kill the play immediately if there is a severe injury, such as an injury involving blood or a hit ball that strikes a defensive player in a vital area.  In this case the umpire will place the runners on the base the umpire believes they would have achieved without the injury.

Tom