public class MyClass
{

    public void deleteOrganization(Organization organization)
    {
        /*Delete organization*/

        /*Delete related users*/
        for (User user : organization.getUsers()) {
            deleteUser(user);
        }
    }

    public void deleteUser(User user)
    {
        /*Delete user logic*/
    }
}

@Test
public void shouldDeleteOrganization()
{
    MyClass spy = spy(new MyClass());

    // avoid invoking the method
    doNothing().when(spy).deleteUser(any(User.class));

    // invoke method under test
    spy.deleteOrganization(new Organization());
}

public void deleteOrganization(Organization organization)
{
    /*Delete organization*/

    /*Delete related users*/
    for (User user : organization.getUsers()) {
        privateDeleteUser(user);
    }
}

private void privateDeleteUser(User user){
   //actual delete logic here, without anything delete organization doesn't need
}


public void deleteUser(User user)
{
    //do validation
   privateDeleteUser(user);
  //perform any extra business locic
}

public void DeleteOrganizationService(){

   private MyClass myClass;
   ...

   public void delete(Organization organization)
   {
       myClass.deleteOrganization(organization);
        /*Delete related users*/
        for (User user : organization.getUsers()) {
            myClass.deleteUser(user);
        }
    }

 }

public void deleteOrganization(Organization organization)
{
    /*Delete organization only does not modify users*/
}

public void deleteUser(User user)
{
    /*same as before*/
}

Self Use of only override-able method is not proper design pattern.

Solution to above problem

public class MyClass
{

    public void deleteOrganization(Organization organization)
    {
        /*Delete organization*/

        /*Delete related users*/
        for (User user : organization.getUsers()) {
            deleteSingleUser(user);
        }
    }

    public void deleteUser(User user)
    {
        deleteSingleUser(user);
    }

   private void deleteSingleUser(User user){
       /*delete user*/
   }
}