Access http://sqeweb.us.oracle.com/net/sqenfs-1/export1/comp/jsn/users/stephen/deployment_stuff/sqe_ws/7/deployment/src/javafx/LiveConnect/LiveConnect/html/EvalTest_null.html, the fx applet inside basically does:
====Begin of Code====
win = getHostServices().getWebContext();
logger.logln("Calling win.eval(" + evalString + ")...");
Object ret = win.eval(evalString);
logger.logln("Done calling:");
====End of Code====

If you see the following behavior on various browsers, then the issue is reproduced.
FF5/GC13: the browser crash
IE7: the IE client JVM hung (waitting at line "Object ret = win.eval(evalString);")

hs_err file for FF and jstack file for IE7 client JVM are also attached.

The same issue could be observed upon calling on win.call(null), too.