Some can veto the mates their families suggest; others choose their own, subject to a parental veto.

分号可起并列连词作用，故本句为并列句：Some...; others...

第二分句中 subject to a parental veto 是形容词短语，为非限制性定语修饰 their own （mates）。该形容词短语相当于一个非限制性定语从句：who are subject to a parental veto.

由此可知，如果在 subject 前加 and， 则为语法错误了。