English equivalent phrase for “To set a fire and also to go and extinguish it”

Solution 1:

As a mental health issue, there is "Munchausen syndrome by proxy," in which a caregiver intentionally harms their ward---so that they can then help them to recover. This lets the caregiver feel wanted (and useful).

(In criminal terms, what you describe could be seen as a type of "forensic countermeasure," where the perpetrator tries to shift suspicion from themself by doing something that they think a criminal wouldn't normally do: return to the scene and provide aid.)

At least in popular media, fictional characters who commit crimes---on the pretence of helping---have been dubbed to have a (coincidentally with what you said) "good Samaritan" motive. But that can either be about ending somebody's suffering or about inflating the criminal's own need for attention and validation.

Perhaps "hero complex," used in a criminal sense, would also apply.

A more accurate response would depend on if the Hindi expression relates to the act itself or a motive behind it.

Solution 2:

That is what false flag means, except that is usually when a state or authority is involved, and an excuse for military action. We sometimes talk about a bogeyman as something created in the same sense, to make its creator appear as protector. We say someone is tilting at windmills when imagining an enemy, straight from Don Quixote.