We will show that factor codes that have a bi-closing word are bi-closing a.e. and have a degree. Moreover, a closing code with a bi-closing word into an irreducible shift space is constant-to-one. Then we study which properties may be invariant by codes that have a bi-closing word under factoring and extension. Moreover, we give some conditions for a bi-closing word and show that every closing open code in an irreducible shift space has a bi-closing word.