When we use the final specifier for a method, the method cannot be overridden in any inherited class. Due to design reasons, the method is finalized. Since private methods are not accessible, they are implicitly final in Java. Therefore, adding the final specifier to the private method does not add any value. It may actually cause unnecessary confusion.

In Java, a private method is a method that can only be accessed from within the same class it is defined in. It cannot be accessed from outside the class, not even from its subclasses. Private methods are often used for internal logic and implementation details that should not be exposed to the outside world.

On the other hand, a final method is a method that cannot be overridden by any subclass. Once a method is declared final, it cannot be modified in any way by any subclass. Final methods are often used when a method is crucial to the functionality of a class, and should not be changed or overridden in any way.

The use of private and final methods can help improve the encapsulation and stability of a Java program. By using private methods, the internal details of a class can be kept hidden and protected from accidental modification or misuse. By using final methods, critical functionality can be locked down and prevented from being modified, ensuring that the behavior of the class remains consistent.

It is important to note that private and final methods can be used together, with a final method that is also private providing the highest level of encapsulation and stability for a class.