The game situation:
- I'm at 12 life, meaning that Death's Shadow is currently a 1/1.
- I'm being attacked by two 2/2 Goblin Guides; I block one of them with the Death's Shadow, leaving the other unblocked.
- We proceed to the Combat Damage step.
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The game situation:
Death's Shadow will survive, because its static ability is "faster" than the state-based action that kills creatures that take lethal damage.
You and Death's Shadow are both assigned 2 damage as described in comp rule 510.1.
That damage is dealt simultaneously (per rule 510.2) and has different effects on players and creatures. Importantly, damage doesn't kill creatures, a state-based action does. State-based actions are only checked when a player gains priority, which no one does at the point in the combat damage step.
120.3a Damage dealt to a player by a source without infect causes that player to lose that much life.
120.3e Damage dealt to a creature by a source with neither wither nor infect causes that much damage to be marked on that creature.
704.5g If a creature has toughness greater than 0, it has damage marked on it, and the total damage marked on it is greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed.
Death's Shadow's static ability, however, doesn't need priority, it simply takes effect. The moment that your life total drops to 10, Death's Shadow becomes 3/3.
Per rule 510.3, after all of the damage is dealt, the active player gains priority and the game checks state-based actions. Because Death's Shadow is a 3/3, 2 damage isn't enough to kill it.
Death's Shadow survives, as do both Goblins. The two Goblins each deal 2 damage (to you and the Shadow, respectively), and Death's Shadow deals 1 damage to the Goblin it was blocking.
The fact it works out this way comes down to some finer details of how we handle combat damage and when creatures die.
The process looks like this:
Let's pause here to review what's just happened. We know that in combat damage, creatures deal damage equal to their power simultaneously to each other & players/planeswalkers, but we can see that when we assign damage in step 2, we've basically locked in the amount of damage that's going to be dealt. It doesn't matter if a creature's power changes in step 3, the damage was already assigned based on what its power was in step 2.
We haven't processed deaths in combat yet, so let's continue:
So to sum up: Death's Shadow is already treated as a 3/3 by the time we finally get to the point of seeing if things will die. We assigned damage, then dealt that damage, then checked the result later, giving your Death's Shadow the capacity to survive.