Prickly wild lettuce, burdock, yellow dock, and amaranth all grow wild in my neighborhood. They’re all edible, and obviously they must be able to grow without irrigation. Purslane grows wild here, too, but mostly only in irrigated spaces, such as lawns and garden beds. It’s a pity it’s not more drought tolerant, because purslane is delicious.
Tepary beans are super duper drought tolerant. I’m planning to plant lots of those next year. I’m planning to do a dry farmed three sisters bed with tepary beans, sorghum, and zucchinis that are used to being dry farmed in Utah. Lauren sent me those seeds. (Thanks, Lauren!)
Echinecea is super drought tolerant. It’s a valuable medicinal herb, and a pretty flower.
Have you tried hollyhocks? There’s a thread talking about them here.
I’m going to be planting banana yuccas in spring. They grow edible fruit. 
It’s supposed to taste delicious!