junit assert in thread throws exception

The JUnit framework captures only assertion errors in the main thread running the test. It is not aware of exceptions from within new spawn threads. In order to do it right, you should communicate the thread's termination state to the main thread. You should synchronize the threads correctly, and use some kind of shared variable to indicate the nested thread's outcome.

EDIT:

Here is a generic solution that can help:

class AsynchTester{
    private Thread thread;
    private AssertionError exc; 

    public AsynchTester(final Runnable runnable){
        thread = new Thread(new Runnable(){
            public void run(){
                try{            
                    runnable.run();
                }catch(AssertionError e){
                    exc = e;
                }
            }
        });
    }

    public void start(){
        thread.start();
    }

    public void test() throws InterruptedException{
        thread.join();
        if (exc != null)
            throw exc;
    }
}

You should pass it the runnable in the constructor, and then you simply call start() to activate, and test() to validate. The test method will wait if necessary, and will throw the assertion error in the main thread's context.

A small improvement to Eyal Schneider's answer:
The ExecutorService allows to submit a Callable and any thrown Exceptions or Errors are rethrown by the returned Future.
Consequently, the test can be written as:

@Test
public void test() throws Exception {
  ExecutorService es = Executors.newSingleThreadExecutor();
  Future<?> future = es.submit(() -> {
    testSomethingThatMightThrowAssertionErrors();
    return null;
  });

  future.get(); // This will rethrow Exceptions and Errors as ExecutionException
}