What is the idiom that can describe the action of making fun of somebody's already sensitive and weak spot for which s/he is already troubled or ashamed?
For instance, mocking somebody about his/her bankruptcy, past crime history, etc.
If you mock someone’s misery, you rub salt into their wounds, described in the Oxford Learner's Dicionary as:
to make a difficult experience even more difficult for somebody
This Dictionary of Idioms gives a fuller definition and example:
Rub salt into the wound/(someone’s) wounds to make (someone’s) sorrow, shame, regret etc worse, often deliberately: I was very disappointed at having to miss the concert, and my friends kept rubbing salt into the wound by telling me how good it was.
And two examples from the media, where rubbing salt into the wound specifically means mocking someone’s misfortune:
City fans mock Manchester rivals: [Manchester] United let a 3-1 lead slip to lose 5-3 at Leicester yesterday, before City took on Chelsea at the Etihad [stadium]. And cheeky Citizens fans took the opportunity to rub salt into their rivals' wounds with an aerial banner. “United we fall ― in cinemas soon," read the message flown over the Eithad.
Hilarious Comeback Joke Takes Off On Reddit After English Mockery: Last week, rugby fans around the world cruelly wallowed in England’s early World Cup exit. Several jokes were posted online and it seemed as if England’s closest neighbours were most keen to rub salt in English wounds.
The idiom add insult to injury is broadly used for the context:
Fig. Cliché, to make a bad situation worse; to hurt the feelings of a person who has already been hurt.
Or add fuel to the fire could be a good candidate:
Fig. to make a problem worse; to say or do something that makes a bad situation worse; to make an angry person get even angrier.
[McGraw-Hill Dictionary of American Idioms and Phrasal Verbs]
The phrase "kicking a man when he's down" comes to mind.
This specifically touches on doing something to exacerbate suffering which should be sufficient on its own.
to do something bad to someone when you know they already have a lot of problems
His wife left him last month and I don't want to kick a man when he's down, but we simply don't have any more work for him.
Cambridge Idioms Dictionary via TFD
If you want to refer to deliberately attacking something that someone is sensitive about, you could say they deliberately touched a nerve
Provoke a reaction by referring to a sensitive topic
Alternatively, you could say they attacked his achilles heel
A weakness or vulnerable point
Both definitions from the OED
One appropriate idiom might be hit where it hurts:
To do something which will upset someone as much as possible
If you want to hit her where it really hurts, tell her she's putting on weight again.
Another might be hit a nerve.
To upset someone by talking about a particular subject
I think I hit a nerve with my comments about divorce. She suddenly looked distressed and I knew I'd touched a raw nerve.
rub someone's nose in it
Bring something, especially an error or fault, repeatedly and forcefully to someone's attention. For example, I know I was wrong, but don't rub my nose in it. This expression alludes to the unkind practice of housebreaking a dog by rubbing its nose in its feces. [Mid-1900s] The American Heritage® Dictionary of Idioms
rub it in
To make someone feel even worse about something; rub salt into somebody's wounds. Cambridge Dictionary of American Idioms
dig up the dirt again/stir up the dirt [on someone]
informal : information about someone that could harm the person's reputation. She's been spreading dirt [=gossip] about her ex-husband.
◊ To dig up (the) dirt on someone is to find out information that is harmful to that person's reputation. He's been digging up dirt on his political rivals. M-W
I'd say it depends on the circumstances. If the person teasing means to stick it to the subject:
Rub salt into the wound.
However, if the subject's been in prison for a violent crime and is more bitter and angry than depressed and sad because of that (hence being prone to erupt):
Poke the bear.
Although sadism is more used for inflicting physical pain, there is nothing to stop it being used for inflicting mental pain, bringing up things that people are trying to forget with the full knowledge that is causing them suffering is sadistic. How ever if somebody is bringing it up to stop one from falling in the same error again is different, so if the intent of mockery is to inflict pain then sadism seems to fit the bill.