P182, "Natural Attacks" section, 2nd paragraph: ..."but only add half your Strength modifier on damage rolls"
For a low Strength Score, the penalty to damage would be halved according to the text above!
This is covered in the combat section.
Off-Hand Weapon: When you deal damage with a weapon in your off hand, you add only 1/2 your Strength bonus. If you have a Strength penalty, the entire penalty applies.