Sturdy
Prevents being KOed from full HP, leaving 1 HP instead. Protects against the one-hit KO moves regardless of HP.
Full effect
When this Pokémon is at full HP, any hit that would knock it out will instead leave it with 1 HP. Regardless of its current HP, it is also immune to the one-hit KO moves: Fissure, Guillotine, Horn Drill, and Sheer Cold. If this Pokémon is holding a Focus Sash, this ability takes precedence and the item will not be consumed.
In game description
The Pokémon cannot be knocked out by a single hit as long as its HP is full. One-hit KO moves will also fail to knock it out.
Pokemon with Sturdy
Geodude
#0075
Graveler
#0076
Golem
#0081
Magnemite
#0082
Magneton
#0095
Onix
#0185
Sudowoodo
#0204
Pineco
#0205
Forretress
#0208
Steelix
#0213
Shuckle
#0227
Skarmory
#0232
Donphan
#0299
Nosepass
#0304
Aron
#0305
Lairon
#0306
Aggron
#0369
Relicanth
hidden
#0377
Regirock
hidden
#0410
Shieldon
#0411
Bastiodon
#0438
Bonsly
#0462
Magnezone
#0476
Probopass
#0524
Roggenrola
#0525
Boldore
#0526
Gigalith
#0539
Sawk
#0557
Dwebble
#0558
Crustle
#0564
Tirtouga
#0565
Carracosta
#0696
Tyrunt
hidden
#0703
Carbink
hidden
#0712
Bergmite
hidden
#0713
Avalugg
hidden
#0777
Togedemaru
hidden
#0790
Cosmoem
#0932
Nacli
#0933
Naclstack
Using Sturdy in Cobblemon
Abilities are passive and always active, so Sturdy costs you nothing to run. If it is marked hidden on a species above, expect it to be harder to obtain: servers differ in whether hidden abilities come from breeding, an Ability Patch, or events.
See the Pokedex for which abilities each species can have, and IVs, EVs and breeding for how to actually pass one down.