Why Is Runtime.runFinalizersOnExit Deprecated?

Because it is inherently unsafe. It may result in finalizers being called on live objects while other threads are concurrently manipulating those objects, resulting in erratic behavior or deadlock. Although this problem could be prevented if the class whose objects are being finalized were coded to "defend against" this call, most programmers do not defend against it. They assume that an object is dead at the time that its finalizer is called.

Further, the call is not "thread safe" in the sense that it sets a VM-global flag. This forces every class with a finalizer to defend against the finalization of live objects!