This is the whole phrase and the sentence I don't understand is in bold:
So "消滅させて" being passive and "サイア人" is the direct object, then "彼らが住む惑星ベジータごと" it's a clause that explain what the Sayajins are/were. ごと could be a nominalizing suffix like:
As to Furiza (...) the sayajins, they who living in the Vejita planet, were sadly extinguished from the universe (by Furiza?).
I don't undestand what they are using the dictionary form for 住む、 and if it's referring to "彼ら", the sayayins or modifying "惑星ベジータ", and i dont understand the use of ごと here.
Thanks form your help.