Cooper has been starting at one of the cornerback positions throughout camp.
The Chiefs were already missing Pro Bowl safety Eric Berry, who hurt his right heel during Thursday's drill. Backup safety Sanders Commings is out after having surgery on a severe high ankle sprain and for a fracture to his fibula.
Reserve defensive backs David Van Dyke, DeMarcus Van Dyke and Phillip Gaines have also missed time with injuries. All the banged-up bodies forced the Chiefs to sign veteran defensive back Steve Gregory earlier this week.
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