Inherit Nested Class.

Base.cs

using UnityEngine;
using System.Collections;
public class Base : MonoBehaviour{
    protected class State
    {
      const int cddc = 0;
    }
}

Inherited.cs

using UnityEngine;
using System.Collections;
public class Inherited : Base 
{
  private class State:Base.State
  {
    const int abba = 100;
  }
    State s;
    public Inherited():base(){
      s = new State();
    }
    public int Member(){
      return s.abba;
    }
    public int OldMember(){
      return s.cddc;
    }
  }

main.cs

--