The property sun.awt.exception.handler and the correspondent mechanism were replaced by an official API in JDK7. It was b49 to be precise. See JDK-4714232 and JDK7 compatibility document, for instance http://www.oracle.com/technetwork/java/javase/compatibility-417013.html
There are still several regression tests setting and depending on this property. They should be rewritten or removed.

java/awt/List/ActionAfterRemove/ActionAfterRemove.java
java/awt/TrayIcon/DragEventSource/DragEventSource.java
java/awt/TrayIcon/DisposeInActionEventTest/DisposeInActionEventTest.java