Sectopods can indirectly bypass Secondary Heart using the Cluster Bomb ability, which critically wounds the soldier, then blows up their body.
Ethereals can kill a soldier with Secondary Heart using the Rift ability, as this ability's AoE damage lasts through the subsequent turn. Any unit critically wounded by the Ethereal's Rift will die at the end of the next turn because of the added AoE damage.
It's possible for EXALTHeavies and Elite Heavies to circumvent Secondary Heart by firing a rocket into a car that the XCOM soldier is using for cover. Assuming that the damage dealt by the rocket plus the damage from the exploding car kills the operative, they will die instead of becoming critically wounded.