There may be more than two answers to this question but I think the characters you are referring to are Mercedes, Dante's former fiance and Mercedes, the Count de Morcerf, wife.  Her spirit was broken by Dante's imprisonment and she lets herself be cajoled into a loveless marriage, thus putting herself under Morcerf's control.  She becomes a wealthy member of society but is miserable.  When she sees Dante and  her husband dies she goes to spend the rest of her house in prayer at a house that had been owned by Dante's father. 

The other character is Monsieur Villeforte.  When his life falls apart and his wife murders their "son" and commits suicide, he goes insane, leaving himself completely in the power of others.

Many other characters lose their will to live but do not leave their lifes in the "control" of others.  Morcerf commits suicide; Heloise Villeforte commits suicide.  Danglers is forgiven and lives but is a ruined man with white hair.  Dante himself does not lose the will to live because his gives control of his life over to the desire for revenge and justice.