When a mob is given a weapon, they inherit the Attribute Modifiers on it. This includes the vanilla modifier for weapon strength, and any custom modifiers. However, when a player ventures too far from that mob, these modifiers are lost.

Steps to Reproduce:

1. Give a zombie a diamond sword. You must have mobGriefing set to true, and must be playing in Normal or Hard mode.
2. When it attacks you, you should experience normal damage - on Normal difficulty, this will be 5 hearts.
3. Move far away from this mob. Using "/tp ~0 ~150 ~0" and letting yourself fall (in Creative!) will distance you enough for this bug to occur.
4. When you let the mob attack you again, it will deal only 1.5 hearts instead of the previous 5.

I have attached a schematic of a bugged zombie, holding an AttributeModifier-laden sword but not bearing its effects. The zombie picked up this sword in-game, and I ventured too far from it. I have also attached a test world of zombies which have lost their Attribute Modifiers for the same reason.