1866, of persons, with reference to health, from verbal phrase, from run (v.) + down (adv.). From 1896 of places; 1894 of clocks. Earliest sense is "oppressed" (1680s).
a run-down neighborhood
a run-down watch
runabout
runaround
runaway
runcible
runcinate
run-down
rundown
rune
rung
runic
run-in