Let's say a character with an 8 STR confirms a critical hit with a short sword. A normal hit for them would deal 1d6-1 damage. Does the critical deal 2d6-2?
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No, it doesn't. The critical deals (1d6-1)+(1d6-1).
I read this as "roll the damage (1d6-1) twice and add together the results". Since a hit always does at least one damage (which might be nonlethal, as below), the damage roll of (1d6-1) has a range of 1-5 damage. This critical hit, therefore, has a range of 2-10 damage. If you roll two 1s then you do 2 nonlethal damage. If you roll 1 and 2 then you do 1 nonlethal and 1 lethal damage. If you roll two 6s then you to 10 lethal damage.
Rolling 2d6-2 is not the same — it has a range of 1-10.
It is the "still deals 1 point of nonlethal damage" which explains why the multiple rolls need to be made separately when there are negative modifiers. Or, to put it another way, doubling (1d6+1) is the same as (2d6+2) but doubling (1d6-1) is not the same as (2d6-2).
Yes, assuming it's a x2 damage weapon
According to Pathfinder SRD
Essentially a critical hit allows you extra damage so while it may be penalized it's still extra. Your mean damage roll would jump from 2 to 5 for what it's worth and because of the extra die it weights towards the center despite the obvious increase in maximum. Normally when negatives aren't included the rules say "bonus (if any)" (e.g. being flat-footed can never increase your AC) to discard negatives although they see it as such a rare occurrence that it doesn't require a special descriptor. In the end, you roll your normal damage a number of times equal to a normal single hit and add it together, thus the multiplier becomes the minimum damage as it's thenumber of damage rolls
From the SRD:
The SRD is very specific, you double your bonus, not your modifier. If your strength is an 8 and you get a -1 penalty to damage, you do not double that since the SRD/books say you double your bonus and not your modifier. Therefore a regular hit would be 1d6-1 and a critical would be 2d6-1 (assuming the weapon multiplier is 2).