Blight Phoenix is the tier 5 skill in Maya's Cataclysm skill tree. Upon killing an enemy you deal constant Fire and Corrosive damage to nearby enemies for a short time. The damage is based on your level of the ability and your level.
Both skills make reference to a Phoenix with the name and the skill icon, and both cause fiery wings to sprout from the Sirens' backs when the skill is active.
It slightly differs mechanically, with an additional instance of corrosive damage dealt with Maya's skill instead of a chance to not consume ammo. However, the fire damage dealt is still there.
Elemental barrels can pose a threat when this skill is active, as passing near them will cause them to detonate, causing damage to the character; make a habit of shooting the barrels first, or avoiding them entirely.
Pairing this skill with Life Tap allows Maya to stay in the middle of the combat area, constantly damaging enemies and heal as well. This tactic can be boosted by also taking Kinetic Reflection, with a +5 class mod, keeping Maya virtually invincible after a kill.
This skill deals damage equivalent to SkillLevel × 1.13PlayerLevel for each individual element. Hence, against a neutral, unshielded target, the total damage would be roughly doubled (elemental damage from both incendiary and corrosive).