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frm_to_be_opened form = new frm_to_be_opened();//call your form as you normally do.
form.FormClosing += new FormClosingEventHandler(methodToBeCalled);//add the FormClosing handler
form.Show();//show your form.

//METHOD THAT IS GOING TO BE EXECUTED ON FORM CLOSING EVENT
private void methodToBeCalled(object sender, EventArgs e){
  //your awesome logic here.
}