You example them as an ‘immigrant’ because an immigrant is someone who comes from another country and moves to a different country.
A run-on sentence usually occurs when two separate sentences or clauses are improperly combined. However, unlike sentence fragments, run-on sentences can still be technically grammatically correct. So technically the are bad.
If the "books" wasn't a plural, it would be "his" but since it isn't singular, it would be "their"