There are problems when working with filters. If you use feathers, try this code. The background skin is disappearing. Everything works with a classic text field.
var container:LayoutGroup = new LayoutGroup();
container.backgroundSkin = new Quad(10, 10, 0xffffff);
container.x = Starling.current.stage.stageWidth * 0.5;
container.y = Starling.current.stage.stageHeight * 0.5;
container.backgroundSkin.filter = new DropShadowFilter();
var textField:ApertureTextField = new ApertureTextField(-1, -1, 'some text', new ApertureTextFormat(ElectricalEngineering.APERTURE_LATO_BITMAP_FONT, 50, 0x0));
// var textField:TextField = new TextField(10, 10, 'some text', new TextFormat(ElectricalEngineering.STYLED_LATO_BITMAP_FONT, 50));
textField.autoSize = TextFieldAutoSize.BOTH_DIRECTIONS;
container.addChild(textField);
container.validate();
this.addChild(container);