This plant looks quite peculiar, very different from the cacti I've seen before. After doing some research, I found out it's called the jumping cholla(Cylindropuntia fulgida). Its branches easily detach and attach to nearby objects or animals, which helps them take root and propagate in different locations. So the scattered pieces on the ground must be its broken-off branches, which will continue to grow and reproduce. What an eye-opener!
Yes, that is the Cholla Cactai. It is native to Sonoran Desert, parts of southern California and northern Mexico. I can confirm that the branches easily detach and get stuck to your clothing :)