Why doesn't this thread pool get garbage collected?

This doesn't really have anything to do with GC being non-deterministic, although it doesn't help! (That is one cause in your example, but even if we 'fixed' it to eat up memory and force a collection, it still wouldn't finalize)

The Worker threads that the executor creates are inner classes that have a reference back to the executor itself. (They need it to be able to see the queue, runstate, etc!) Running threads are not garbage collected, so with each Thread in the pool having that reference, they will keep the executor alive until all threads are dead. If you don't manually do something to stop the threads, they will keep running forever and your JVM will never shut down.

Affe is correct; the thread pool's threads will keep it from being garbage collected. When you call Executors.newFixedThreadPool(3) you get a ThreadPoolExecutor constructed like so:

ThreadPoolExecutor(3, 3, 0L, TimeUnit.MILLISECONDS, new LinkedBlockingQueue<Runnable>());

And if you read the JavaDoc for ThreadPoolExecutor it says:

A pool that is no longer referenced in a program AND has no remaining threads will be shutdown automatically. If you would like to ensure that unreferenced pools are reclaimed even if users forget to call shutdown(), then you must arrange that unused threads eventually die, by setting appropriate keep-alive times, using a lower bound of zero core threads and/or setting allowCoreThreadTimeOut(boolean).

If you want your thread pool to finalize like you're expecting, you should do one of those things.