She suffered terribly after her husband died on her.
Literal
Husband [by-に] died-on-her [and-て] she [topic-は] terribly suffered.
夫に死なれて is the adversative passive: 'had her husband die on her.' The passive frames the death as something that happened to her disadvantage — a powerful grammatical expression of loss. ひどく苦しんだ = 'suffered terribly.'