Consider the following test case (source is below): two windows, one is a pure JavaFX window that acts as a drag source, another is a Swing window with FX embedded using JFXPanel that acts as a drop target. Dragging from FX to Swing 100% deadlocks in this scenario.

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            JFrame f = new JFrame("F");
            f.setBounds(400, 100, 320, 240);

            JFXPanel p1 = new JFXPanel();
            Platform.runLater(() -> {
                Text t = new Text("Drag from here");
                t.setStyle("-fx-font-size: 32px");
                t.setOnDragDetected(new EventHandler<MouseEvent>() {
                    @Override
                    public void handle(MouseEvent event) {
                        Dragboard db = t.startDragAndDrop(TransferMode.COPY);
                        ClipboardContent content = new ClipboardContent();
                        content.putString("FX TEXT");
                        db.setContent(content);
                        event.consume();
                    }
                });
                t.setOnDragDone(new EventHandler<DragEvent>() {
                    @Override
                    public void handle(DragEvent event) {
                        t.setText("Drag done");
                    }
                });
                Scene s = new Scene(new FlowPane(t), Color.RED);
                p1.setScene(s);
            });
            f.add(p1);
            f.setVisible(true);

            JFrame g = new JFrame("Swing");
            g.setBounds(400, 500, 320, 240);
            JFXPanel p2 = new JFXPanel();
            Platform.runLater(() -> {
                Text t = new Text("Drop here");
                t.setStyle("-fx-font-size: 32px");
                t.setOnDragEntered(new EventHandler<DragEvent>() {
                    @Override
                    public void handle(DragEvent event) {
                        event.acceptTransferModes(TransferMode.ANY);
                        event.consume();
                    }
                });
                t.setOnDragOver((event) -> {
                    event.acceptTransferModes(TransferMode.ANY);
                    event.consume();
                });
                t.setOnDragDropped(new EventHandler<DragEvent>() {
                    @Override
                    public void handle(DragEvent event) {
                        t.setText(event.getDragboard().getString());
                        event.setDropCompleted(true);
                        event.consume();
                    }
                });
                Scene s = new Scene(new FlowPane(t), Color.BLUE);
                p2.setScene(s);
            });
            g.add(p2);
            g.setVisible(true);
        });
    }

Other 3 combinations (dragging from FX to FX, from JFXPanel to FX, and from JFXPanel to JFXPanel) work fine (the last is fixed in RT-28347).