There was never any barley bread left over from the household of the Prophet ﷺ.
ما كان يفضل عن أهل بيت النبي ﷺ خبز الشعير.
Tirmidhi narrated it in his Jami (2359) and in Shamail (144), and Ahmad (22244), both through Hurayz bin Uthman (he is Rahbi), from Salim bin Amir who said, I heard Abu Umama say, and he related it. Its chain of transmission is sahih. Tirmidhi said, "This is a hasan sahih hadith, gharib from this route."