Using JQuery, you can trigger a custom event.
An example according to your code:
_ebSaveDialogue: function () {
//Saving Dialogue
$('#ebDialogueClose').click(function () {
var text = $('#ebPlaceholder').val();
returnText = text;
$('#ebDialogue_div').dialog("close");
$('#ebDialogue_div').trigger('save_action', returnText);
});
}
Then, from any other point in your script, you set an event listener for that event
$('#ebDialogue_div').on('save_action', function(event, returnText){
alert(returnText);
});