The Soul Sabre has this ability. It damages the target's MP and the user is healed for an equivalent amount of MP when attacking.
The MP Absorb Materia is a Support Materia that restores the user's MP when the paired ability is used. The amount restored is 1% of the damage dealt, but if the ability heals the target, MP Absorb will hurt the character instead.
When linked to Magic and Summon Materia, MP Absorb will apply its effect to all abilities the Materia grants. When linked with a regular Command Materia, MP Absorb will apply its effect to the ability that is highlighted on the Materia. The darkened ability will only gain the effect if the character has another source for that ability; for example, if a character has Level 2 Throw, which grants Coin, the MP Absorb applies to Coin only, and not Throw, unless the character also equips another Throw Materia at Level 1.
When linked with Master Command, MP Absorb will apply its effect to all commands in the Materia, plus the Attack and Item commands. Throw is exempt unless the character has another source for the Throw ability, since Master Command doesn't support Throw as a separate ability. Equipping MP Absorb with Master Command allows the character to gain MP for performing regular attacks, but using healing items and magic will damage the user's MP equal of 1% of gained health.
The MP Absorb Materia will not work with the Enemy Skill Materia.
Absorb MP is an support ability exclusive to Quina. When Quina has no MP, s/he gains some MP when struck by an enemy's spell. The amount of MP restored is equal to the MP needed to cast that spell. Absorb MP is learned from Promist Ring for 80 AP and takes six Magic Stones to equip.
Absorb MP from one enemy.
Recover MP equal to the amount used by the opponent.
Absorbs MP used to cast a spell against you.
Magic Thirst is a Vampirism ability learned by Vampires at job level 6. It allows the character to absorb from one target an amount of MP equal to 10% of the damage dealt a normal attack.