There could be several reasons. One possibility is that they are in some kind of trouble themselves and think blackmailing the mom can solve their problems. For example, they might have debts they need to pay off. Another reason could be that they are just bad - natured kids. They might enjoy having power over someone and see blackmail as a way to get that power. Or perhaps they have some secrets that they don't want the son to know and they are using blackmail to keep the mom quiet about those secrets.
That's a very serious and unethical situation. Here is a possible story: One day, a person found out a secret about his friend's mom. Instead of handling it in a proper way, he tried to blackmail her by threatening to reveal the secret if she didn't give him money. The mom was terrified at first but then decided to be brave and told her family. Together, they went to the police and the blackmailer was caught in the end.
Another motive could be revenge. Maybe he has some grudge against the son and he thinks blackmailing the mom is a way to get back at him. He figures it will cause chaos in the family and make the son unhappy.
Well, in such a story, it's likely that the son got into financial trouble, perhaps through bad business decisions or irresponsible spending. And the people he owed money to saw the mom as an easy target to get the money from, so they blackmailed her. For example, they could have told her that if she didn't pay, they would damage the son's reputation or even take legal action against him which would put the whole family in a difficult situation.
Well, perhaps the son has some financial problems and he blackmails his mom by threatening to expose a family secret that she has been keeping hidden. It could be something that would make the family look bad in the community, so she is forced to comply with his demands.
Well, it could be that the son's friend has some sort of secret about the mom that he's using to blackmail her. Maybe she made a mistake in the past that she doesn't want her son or others to know about.
Since we only know the basic premise of the'mom blackmailed to pay son's debt story', the blackmailers could be anyone. They might be people the son met in a gambling situation if he had a gambling problem and owed money. Or they could be part of an organized crime group that preys on vulnerable people like the mom by using her son's debt as leverage.