I guess O.Henry is coining words. He is describing a man apparently with far advanced tuberculosis, and describes him as "debile". Not in dictionary, except as botanical epithet, meaning weak, feeble, etc.

"So, then, it was no surprise to the ranchhold when the buckboard spun to the door, and Raidler took up his debile protege like a handful of rags and set him down upon the gallery."

Debile adj. Weak, feeble, suffering from debility.

OED First cite 1536, last 1890

The D volume was done from 1893-1897