Is there a card that has opponents discard cards whenever they lose life?
No, as this search reveals.

Noteable:


Mindcrank: "Whenever an opponent loses life, that player puts that many cards from the top of their library into their graveyard." Extremely close to what you requested, but it doesn't trigger Fell Specter's ability.
Exquisite Blood: "Whenever an opponent loses life, you gain that much life." It forms a similar combo with Sanguine Bond and Epicure of Blood instead of Fell Specter.