I Control a Dusk Urchins that currently has two -1/-1 counters on it when I play a Skinrender targeting the Urchins with its minus counters. How many counters would the Dusk Urchins second triggered ability count, the minimum to reduce its toughness to zero (three) or the total number of minus counters (five)? I believe all the counters would be placed and the creature put into the graveyard as a state based action resulting in a count of five -1/-1 counters.
The Urchins die with 5 -1/-1 counters, so you get to draw 5 cards. When state based actions check after the Skinrender's trigger resolved, they see a -1/-2 creature, and since the toughness is equal to or less than 0, it is put into its owner's graveyard. Power and toughness can be reduced to less than 0, the game has no problem with that per se, state based actions will just kill the creature with too low a toughness. Likewise, the rules can handle negative power and make a creature with less than 0 power deal no combat damage, not negative combat damage.
Dusk Urchins counts the number of -1/-1 counters it had on it when it died. Not the number that was necessary to reduce its toughness to exactly zero. Also, you're definitely getting all of those -1/-1 counters because (a) Skinrender's ability puts them all on at once, and (b) even if it didn't, as you note, Urchins doesn't die until SBAs are checked after the ability has finished resolving.
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Dusk Urchins counts the number of -1/-1 counters it had on it when it died. Not the number that was necessary to reduce its toughness to exactly zero. Also, you're definitely getting all of those -1/-1 counters because (a) Skinrender's ability puts them all on at once, and (b) even if it didn't, as you note, Urchins doesn't die until SBAs are checked after the ability has finished resolving.