For «زَيْدٌ فِي الدَّارِ», grammatical explanation may reconstruct an understood verb «اسْتَقَرَّ» or an understood participle «مُسْتَقِرٌّ».
The source specifically mentions the verbal reconstruction. Neither reconstruction is an extra overt word in the sentence. They explain how the locative phrase is predicated of Zayd.