Handle the closing of an App on Android

What you are doing is completely eliminating the execution of the application in memory, therefore when you start it will open with its initial state.  If you want to save the status, you should save some values using some storage method (database, preferences, files), but you should consider that if you want to save a session depending on how sensitive your credential information is, you could even consider saving the session through a webservice.

This is a simple example where using the value of a preference determines that you open at the beginning of the application, the screen to authenticate or the main screen of the application when you have credentials:

//Obtiene valor de sesion activa.
boolean sesionActiva = obtieneValorSesion(getApplicationContext());

//Valida si muestra pantalla de Login o MainActivity desde una Splash Activity.
if(sesionActiva){ 
  //Abre pantalla principal.
  Intent myIntent = new Intent(SplashActivity.this, MainActivity.class);
  startActivity(myIntent);      
}else{
  //Abre pantalla para autenticarse.
  Intent myIntent = new Intent(SplashActivity.this, LoginActivity.class);
  startActivity(myIntent);
}

The methods required to save the value of the session would be:

private String PREFS_KEY = "mispreferencias";

public void guardaValorSesion(Context context, Boolean valorsesion) {
    SharedPreferences settings = context.getSharedPreferences(PREFS_KEY, MODE_PRIVATE);
    SharedPreferences.Editor editor;
    editor = settings.edit();
    editor.putBoolean("sesion", valorsesion);
    editor.commit();
}

public boolean obtieneValorSesion(Context context) {
    SharedPreferences preferences = context.getSharedPreferences(PREFS_KEY, MODE_PRIVATE);
    return  preferences.getBoolean("sesion", false); //valor default false
}

If you want to persist the status of your activities, you can review the life cycle of Activity .

• Implement the persistence of your activity status in onStop() or onPause() .
• Implement state rebuild in onStart() or onPause() .

So you stay with an application that keeps your data independent if it is interrupted by another activity, closed by the user or deleted by memory usage.