use this script it will help to remove only the empty text frame

var myDocument = app.activeDocument;
var myStories = app.activeDocument.stories.everyItem().getElements();
for (i = myStories.length - 1; i >= 0; i--){
    var myTextFrames = myStories[i].textContainers;
    for (j = myTextFrames.length - 1; j >= 0; j--)    {
var stroke = myTextFrames[j].strokeWeight;
var color = myTextFrames[j].fillColor.name;
//alert (color)
     if (myTextFrames[j].contents == "" && stroke == "0" && color == "None"){
           //alert ("yes") 
   myTextFrames[j].remove();
        }
    }
}
 

@winterm:
You can try this using script menu actions. This will only work, if the certain menu action is available.
It is not available if there is contents in the text frame (e.g. a blank character) or (much more important from a scripters point of view) if a threaded text frame is empty because it's contents cannot fit inside it and it's contents is an empty string.

Following code will single out empty text frames, select them and invoke a script menu action to set them to "Unassigned":

var _d = app.documents[0];
var _allStories = _d.stories;
 
 
for(var n=_allStories.length-1;n>=0;n--){
    var _storyAllTextFrames = _allStories[n].textContainers;
 
    for(var m=_storyAllTextFrames.length-1;m>=0;m--){
        //If the contents of a text frame is an empty string:
        if(_storyAllTextFrames[m].contents === ""){
            _storyAllTextFrames[m].select();
            //Convert frame to "Unassigned":
            try{
            app.scriptMenuActions.itemByID(11297).invoke();
                }catch(e){};
            };
        };
    };
 
//Trick to deselect the last selection
//Add a new textFrame, select and remove it:
var _tempTextFrame = _d.textFrames.add();
_tempTextFrame.select();
_tempTextFrame.remove();

@all: If there is a better way to deselect a selection please give an example…

Uwe

1. Use ContentType:

_storyAllTextFrames[m].contentType = ContentType.UNASSIGNED;

2. Use app.select:

void select (selectableItems: varies[, existingSelection: SelectionOptions=SelectionOptions.REPLACE_WITH])
Selects the specified object(s).

app.select(NothingEnum.NOTHING);

(Edit: Hi Marijan!)