The phrase "already run down" is correct and usable in written English.
It can be used to describe something that has been depleted, exhausted, or diminished in quality or condition prior to the current moment.
Example: "After years of neglect, the old building is already run down and in need of major repairs."
Alternatives: "already worn out" or "already deteriorated".
The movement had already run down before the war started.
Anne Hawley, the director of the Gardner Museum, said that through the years the museum had dealt with many writers and filmmakers consumed by the theft, but that with perhaps 1,000 leads already run down, her optimism was tempered by realism.
The father had already run down the stairs, she said, in shock and covered in blood.
They have already run down their inventories and are trimming investment and jobs.
We've already run down some of 2011's best photos, music, art, theater and shopping of the year, but as we kick off the first week of the new year, we had just one final year-in-review piece to offer.
This was a president unbound from much of what defined him upon taking office four years ago, a man clearly cognizant of time already running down on his opportunity to make his imprint on the country and on history.
He is already running down the hall toward the perfect summer day.
He said many local authorities were already running down their careers services, known as Connexions, because they are ceasing to have a statutory duty to provide them from next year.
The American conglomerate, which already owns the Milka and Toblerone chocolate brands, said would it grant a reprieve to workers at the Cadbury plant in Somerdale, near Bristol, where production was already being run down ahead of its planned closure.
If you are already feeling run down after two and a half years slogging it out day-in, day-out with Mother Nature, you'll need to tap into all your reserves for this final push.
A year later, the Times audited the country, describing the first bookmakers' shops, and reporting on the genteel (a "clean, sky-blue parlour") as well as the already run-down (a "seedy, litter-strewn room containing listless youths sucking pencils").
