There is no evidence to suggest that such immoral and disturbing situations are common or real in general. These types of stories might be fictional or extremely rare deviant cases. In a normal family environment, such behavior is completely unacceptable and goes against basic moral and ethical norms.
One possible story could be that a son discovers his mom's secret affair in the past. Instead of handling it maturely, he blackmails her into giving him a large sum of money to keep it quiet. The mom, fearing the exposure and its consequences on her family and reputation, is forced to comply.
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.
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.
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.
Communication is key. The mother and son need to sit down and have an honest conversation about what is going on. The son should be made to understand the seriousness of his actions.