FULL PRODUCT VERSION :
java version "1.8.0_05"
Java(TM) SE Runtime Environment (build 1.8.0_05-b13)
Java HotSpot(TM) 64-Bit Server VM (build 25.5-b02, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Microsoft Windows [Version 6.1.7601]

EXTRA RELEVANT SYSTEM CONFIGURATION :
Using a custom keyboard layout named Programmer Dvorak (http://www.kaufmann.no/roland/dvorak/). The key between left Shift and Z as the keys are called on a QWERTY layout (scancode 82 = 0x56) is translated to VK_OEM_102. This VK is then translated to a dead key 0x0004 (it's functionality is similar to that of the compose key). The character is EOT. I've also tried it (with the same result) with the 0x0002 key (STX).

A DESCRIPTION OF THE PROBLEM :
The key between left shift and Z (as they are called on a QWERTY layout) is not detected by Java when it is a dead key. This key works fine in most applications, but in Java applications, pushing it usually has no effect. I'm using a modified version of the Programmer Dvorak keyboard layout, but this is a problem with the "original" layout as well (version 1.2.4). 

When I switched the key to not be a dead key, but instead a '<' character, it worked as expected (When pressed, it would print the <. The unexpected thing was, that Java now saw it as VK_LESS).
When I changed the character mapping to 0x0002 (which I know worked correctly when used as a dead key located at AltGr+M), it did not get detected (it said VK_UNDEFINED).
Then I changed it's mapping to '<' in default position and 0x0002 in Shift position. It worked as expected in MS Notepad. In Java it didn't work as a dead key (Java saw 0x0 as the character) but worked as a < key.

Note: For debugging my test application I System.out.println'd the KeyEvents. I only saw these lines on my coding PC, not the one I used to test the keyboard layout (that requires lots of reboots). There I only tried it with the original (unmodified) Programmer Dvorak keyboard layout. Here is the relevant output line (I coldn't copy the control EOT character - here I replaced it with the text EOT):

java.awt.event.KeyEvent[KEY_PRESSED,keyCode=0,keyText=Unknown keyCode: 0x0,keyChar='EOT',keyLocation=KEY_LOCATION_STANDARD,rawCode=226,primaryLevelUnicode=4,scancode=86,extendedKeyCode=0x0] on javax.swing.JTable[,0,0,450x400,alignmentX=0.0,alignmentY=0.0,border=,flags=251658568,maximumSize=,minimumSize=,preferredSize=,autoCreateColumnsFromModel=true,autoResizeMode=AUTO_RESIZE_SUBSEQUENT_COLUMNS,cellSelectionEnabled=false,editingColumn=-1,editingRow=-1,gridColor=javax.swing.plaf.ColorUIResource[r=122,g=138,b=153],preferredViewportSize=java.awt.Dimension[width=450,height=400],rowHeight=16,rowMargin=1,rowSelectionAllowed=true,selectionBackground=javax.swing.plaf.ColorUIResource[r=184,g=207,b=229],selectionForeground=sun.swing.PrintColorUIResource[r=51,g=51,b=51],showHorizontalLines=true,showVerticalLines=true]

My conclusion: Java detects keys based on their primaryLevelUnicode, which is the character of the key in a non-modified position. It can detect dead control-character keys, but not in the OEM_102 position.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
Install and enable the Programmer Dvorak keyboard layout (linked above).

Open a Java application with a JFrame that has this structure: JFrame->JPanel->JTextPane

Click into the text pane to start writing text.

Push the OEM_102 key (between LShift and Z on QWERTY keyboards).
Push the C key twice.

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
The '��' character being written. (U+010D)
ACTUAL -
The 'c' character written twice. (U+0063)

REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
package nulano.kblutil;

import javax.swing.*;
import java.awt.*;

public class InputBox {
	private JPanel panel1;
	private JTextPane typeTextHereTextPane;

	{
// GUI initializer generated by IntelliJ IDEA GUI Designer
// >>> IMPORTANT!! <<<
// DO NOT EDIT OR ADD ANY CODE HERE!
		$$$setupUI$$$();
	}

	/**
	 * Method generated by IntelliJ IDEA GUI Designer
	 * >>> IMPORTANT!! <<<
	 * DO NOT edit this method OR call it in your code!
	 *
	 * @noinspection ALL
	 */
	private void $$$setupUI$$$() {
		panel1 = new JPanel();
		panel1.setLayout(new BorderLayout(0, 0));
		typeTextHereTextPane = new JTextPane();
		typeTextHereTextPane.setText("Type text here...");
		panel1.add(typeTextHereTextPane, BorderLayout.CENTER);
	}

	public static void main(String[] args) {
		JFrame frame = new JFrame("Input Box");
		frame.setContentPane(new InputBox().panel1);
		frame.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);
		frame.pack();
		frame.setVisible(true);
	}

}

---------- END SOURCE ----------