Caroline and her husband had borrowed money from Scrooge and were not able to pay it back in time. Scrooge refused to give them any extension, despite the poor circumstances the family lived in.
When the third spirit visits Scrooge, it makes him witness his cleaning lady gleefully selling off some of his belongings. He is so horrified that he asks the spirit, “If there is any person in the town, who feels emotion caused by this man's death, show that person to me, Spirit, I beseech you!” In response the spirit takes him to Caroline’s house.
She is worriedly pacing the floor awaiting her husband with news of Scrooge’s answer to their request for extra time to pay back the loan. In this time, people who did not pay back debts were thrown in prison, often with their families. Scrooge had the power to put the entire family behind bars for an indeterminate time, at least until the debt was paid back. That was often impossible unless a friend or relative helped out, since one wouldn’t be making any money in jail. Caroline is right to be so nervous.
When her husband arrives with the news that Scrooge is dead, Caroline is happy, then she feels bad for being happy at a man’s death. “…she was thankful in her soul to hear it, and she said so, with clasped hands. She prayed forgiveness the next moment, and was sorry; but the first was the emotion of her heart.”
They have good reason to be happy. Now they won’t be sent to jail. Their debt is not erased; someone else will acquire it when Scrooge’s business is sold after his death, but that gives them plenty of time to get the money. Even if they don’t, Caroline’s husband points out that another creditor would not be as merciless as Scrooge.
The narrator sums up their feelings this way: “Soften it as they would, their hearts were lighter. The children's faces, hushed and clustered round to hear what they so little understood, were brighter; and it was a happier house for this man's death! The only emotion that the Ghost could show him, caused by the event, was one of pleasure.”
Realizing that his death caused people happiness had a powerful effect on Scrooge and went far in convincing him to change his ways.