From the Core Rulebook,
« A critical hit means that you roll your damage more than once, with all your usual bonuses, and add the rolls together. »
There is nothing about the sign of the STR modifier.
The damage roll of a critical hit is described as [ weapon's damage die/dice + relevant Char. mod.] x weapon's crit. multiplier, not as weapon's damage die/dice x weapon's crit. multiplier + relevant Char. mod.
"you roll your damage more than once", that's what the rules say, that's what you do. The -1 is part of the damage roll, and thus applied more than once as well.
From the Core Rulebook,
« A critical hit means that you roll your damage more than once, with all your usual bonuses, and add the rolls together. »
Is a -1 modifier a 'bonus'? Sounds more like a penalty to me...
I'm sure the correct answer is that damage penalties get multiplied too, but I can see how the idea that they don't might have got started.
It is indeed a penalty and not a bonus, but the subordinate clause about bonuses is only an explanation for the main sentence.
Yes, it should have been writter clearer (something you can say about half the CRB, sadly). It gets espesially bad if you run into the "if your damage is below 1, you deal 1 nonlethal damage" rule in combinaiton with critical hits.