STR damage can be recovered at the rate of 1 per day per point below the character's natural STR. That is to say a character recovering 1 STR point in damage could recover it in one day, while a character recovering 3 STR below their total would take 3+2+1 or 6 days to recover their full health.I just made that shit up.
However, recently I had a chance to test it. The party was fleeing down a cavern while being pursued by hobgoblins and the fighter decided to stop and bust open a crate despite warnings from the others to hurry onward. The hobgoblins rushed around the corner and started peppering her with arrows and she took 35 points of damage, 12 points more than the 23 HP she had. She immediately fell unconscious and dropped from 16 to 4 STR. She would have quickly died had not the mage reluctantly turned and cast a web spell entangling the Hobgoblins in the corridor and allowing the party to hurriedly administer a healing potion and half carry her to safety. The potion healed her back up to 6 HP but her STR was still 4 (STR bonus -3, a splint mail DEX penalty -12 making it unwearable and weapon penalty of -8) and she was almost helpless. It will take her 12 days to gain back that first STR point. In total it will take 78 days for her to be back at full STR. 50 days just to get back to an average strength of 9.
I think that works. I believe that represents the catastrophic damage she took without being too realistic or saddling the character with permanent disabilities. And of course she could still adventure with only 9 STR if she had to and this rate could be sped up at the GM's discretion if she spent time in a monastery of healers or if there were potions or other magic available to heal her faster. I bet after all that she'll listen to her companions when they are screaming at her to leave the shiney box alone and run the hell away.
By the way they are still in that cavern, hiding up on a dusty ledge that leads off into darkness and full of thick sticky cobwebs...