Run attached code:

import java.util.HashMap;
import java.util.Map;
import javafx.application.Application;
import javafx.scene.input.Clipboard;
import javafx.scene.input.ClipboardContent;
import javafx.scene.input.DataFormat;
import javafx.stage.Stage;

public class DnD extends Application {

    final static Map<DataFormat, Object> receivedContent = new HashMap<DataFormat, Object>();

    @Override
    public void start(Stage stage) {
        ClipboardContent content = new ClipboardContent();
        DataFormat DF_CUSTOM_STRING = new DataFormat("dndwithcontrols.custom.string");
        String CONTENT_CUSTOM_STRING = "Hello Custom String!";
        content.put(DF_CUSTOM_STRING, CONTENT_CUSTOM_STRING);
        Clipboard.getSystemClipboard().setContent(content);
        receivedContent.put(DF_CUSTOM_STRING, Clipboard.getSystemClipboard().getContent(DF_CUSTOM_STRING));
        //String s = (String) Clipboard.getSystemClipboard().getContent(DF_CUSTOM_STRING);
    }

    public static void main(String[] args) {
        Application.launch(args);
    }
}

I see fatal error:
# A fatal error has been detected by the Java Runtime Environment:
#
# SIGSEGV (0xb) at pc=0xb6f36f0c, pid=13992, tid=2099002224
#
# JRE version: 7.0-b146
# Java VM: OpenJDK Server VM (21.0-b16 mixed mode linux-x86 )
# Problematic frame:
# V [libjvm.so+0x3f1f0c] jni_IsInstanceOf+0x8c
#
# Failed to write core dump. Core dumps have been disabled. To enable core dumping, try "ulimit -c unlimited" before starting Java again
#
# An error report file with more information is saved as:
# /home/fx/NetBeansProjects/CoordinatesIssue/hs_err_pid13992.log
#
# If you would like to submit a bug report, please visit:
# http://bugreport.sun.com/bugreport/crash.jsp
#
Java Result: 134

Not reproducible with jdk6. And reproducible with JDK7.