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Context: stealthy sniper advanced rogue talent reduces sniping check to -10. Expert sniper feat reduces the penalty by 10. The 5 rank skill unlock for stealth also reduces the penalty for sniping by 10.

Since the penalty is reduced by 10 from 0, does it become a +10 bonus? Existing Pathfinder logic tells me no. But if I am supposed to get a +10 bonus to sniping, there's no way I'll miss out.

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There is no negative bonus, just as there is no positive penalty.

This is actually spelled out explicitly for ability scores in the text. From the PRD, under ability scores:

Each ability, after changes made because of race, has a modifier ranging from –5 to +5. Table: Ability Modifiers and Bonus Spells shows the modifier for each score. The modifier is the number you apply to the die roll when your character tries to do something related to that ability. You also use the modifier with some numbers that aren't die rolls. A positive modifier is called a bonus, and a negative modifier is called a penalty.

Under combat, Armor Class, there's is also this clarification:

Sometimes you can't use your Dexterity bonus (if you have one). If you can't react to a blow, you can't use your Dexterity bonus to AC. If you don't have a Dexterity bonus, your AC does not change.

Which means that you lose your dexterity bonus when surprised, but you do not lose your dexterity penalty.

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Almost certainly no, "penalty may not be reduced below zero" is the general rule found in the small print for abilities that reduce penalties, I believe it is also a clause in the general rules along with what bonuses stack etc... but I couldn't give you a page number to find that on. There may be exceptions but I've never heard of any.

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