stop, suspend, resume are @deprecated. Но если нужно, что тогда?

Если такой функционал нужен, то его нужно реализовывать через флаги.

public class App extends Thread {

  static App self;

  private volatile boolean threadSuspended = false;

  public App(String name) {
    super(name);
  }

  public static void main(String[] args) {

    self = new App("WORKER");

    self.start();

    new Thread(new Runnable() {
      public void run() {
        try {
          Thread.sleep(5000);
          printFromThread("Let's suspend!");
          self._suspend();

          Thread.sleep(5000);
          printFromThread("Let's resume!");
          self._resume();

          Thread.sleep(15000);
          printFromThread("Let's stop!");
          self._stop();

          Thread.sleep(15000);
          printFromThread("I'm going to die...");

        } catch (InterruptedException e) {
          printFromThread("Interrupter is interrupted!!!))))))))))))))))))");
        }
      }
    }, "controller").start();
  }

  private static void printFromThread(String x) {
    System.out.println( "[ " + Thread.currentThread().getName() + " (" + System.nanoTime() + ") ]" + x);
  }

  public void run() {
    Thread thisThread = Thread.currentThread();
    while (self == thisThread) {
      try {
        printFromThread("I'm starting sleeping");
        Thread.sleep(1000);
        printFromThread("I've just finished sleeping");

        synchronized (this) {
          printFromThread("I'm just synchronized");
          while (threadSuspended && self == thisThread) {
            printFromThread("Let's start waiting iteration");
            this.wait();
            printFromThread("Good morning!.....");
          }
        }
      } catch (InterruptedException e) {
        printFromThread("Look's like I was awoken now!");
      }
      repaint();
    }
  }

  public void repaint() {
    printFromThread("<<<<<<<<<<<<<<<<<<< Repainting ... >>>>>>>>>>>>>>>>>>>>>>");
  }

  public synchronized void _suspend() {
    printFromThread("self was suspended.");
    threadSuspended = true;
  }

  public synchronized void _resume() {
    printFromThread("self was resumed");
    threadSuspended = false;
    notify();
  }

  public synchronized void _stop() {
    self = null;
    printFromThread("self was \"nulled\". So let's notify to break wait");
    notify();
  }
}