Pattern to communicate with a thread

I have a class OuterClass that contains a List and there is a thread ListWorker that is started in OuterClass that is adding some elements to the list. Based on a function call to OuterClass , it should be able to inform the thread to delete elements. What is the best practise? The intention is not to have a blocking data structure (no synchronization) and therefore having a single thread work on List.

Class OuterClass {
    List<String> list = new ArrayList<String>();
    ListWorker worker = new ListWorker(list);

    deleteLastElement() {
        worker.setDeleteLastElement(true);
    }
}

The worker

ListWorker implements Runnable {

private List<String> list;
private volatile boolean deleteLastElement;

public void setDeleteLastElement(boolean deleteLastElement) {
    this.deleteLastElement = deleteLastElement; 
}

public ListWorker(List<String> list) {
   this.list = list;
}

public void run() {
while(true) {
    //add random elements

    if(deleteLastElement) {
     //delete last element
     //set the boolean now to false
    }
  }
}