If one dies, they will cast Arise, reviving the other dead Purobolos. This can make the battle long and tedious for an unprepared party. They use Self-Destruct in low HP, forgoing Arise. Purobolos are weak against Silence.
The best strategy is to use multi-target magic to kill them at once. Black Mages and Summoners should cast their highest level magic and a Blue Mage can help by using Aqua Breath or multi-target Aera. Ninjas can contribute by throwing scrolls. Another way to secure a victory is to use the Samurai ability Gil Toss depending on how much gil the party is willing to part with.
Another method is to take advantage of their Self-Destruct, as that stops them from casting Arise. Characters with physical-based jobs should attack each one separately until their HP is low, minimizing the damage from Self-Destruct.
In the event of a worst-case scenario (i.e. a completely unprepared party), it is possible to constantly kill them until they run out of MP for Arise.
The Blue Mage and a Beastmaster make this battle simpler; Control can be used to force them to Self-Destruct, and Missile is an excellent way to damage them without killing them. Magic Hammer drains their MP so they cannot cast Arise.
The piroboli were mythological living stones that could be found near volcanoes, and when brought near each other would burst into flames.