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Defense shredding below that lowers the starting defense concept per enemy. As it says in game, Defense shredding can take an enemies defense below zero, where you can start off doing more damage beyond that base pierce stat. So if defense is at 2 and defense piercing is 1 then the enemy still has 1 defense before the final damage you do at the top of your stat page.
If defense shredding has a percentile it ignores that percent of the leftover 1 defense (where we started at 2) ... then your final damage is applied.
Defense piercing scaling is like your damage multiplier where it multiplies that base defense piercing number. That output is after your defense shredding is applied (I think) ... and if you have a real high defense shredding then, you can do damage as needed separate from your final damage output.
So say your power/damage approach isn't working too well for whatever reason, try boosting your defense piercing/shredding stat through cards or gear, or getting different types of weapons.
Hope that helps some until somebody else gives a more effective explanation.
So, say a starting damage multiplier on a weapon like death aura is .05 (go to your weapon list during a run and select or click on it, a menu will come up) ... that value is the weapon damage multiplier at that weapons' level. Katana, thorn, and all the others will have their own damage multiplier for each weapon depending on the weapons' level.
Defense piercing scaling is essential for later game challenges. Some of the challenges reduce your power/damage either per level or per stage. So a rog can end up dealing very little damage until getting used to the difference between the two.