'The Conspiracy' is a fan-name for the suggested 'rich and powerful backers' who seem to be trying to assassinate Van Helsinki throughout the fanfictions. That such a group exists seems certain, though exact details and confirmation remain vague. However, more seems to be being revealed in the current Van Helsinki: The Hunt storyline.
The conspiracy appears to have hired out 'Vladimir' and then givne him money to fund a large assault on Van Helsinki as he finished the Case against Albulka. 'Vladimir' attempted to capture him, but his attempts were foiled by Van and his partner, Sophia.
After Van returned from his 'Grand Hiatus' and rejoined the police force, a squad of professional assassins were sent to kill him in his hospital room. However, Van managed to outsmart them and instead killed them, leaving their only victims as some police guards.
Later, the attempts heated up, with attempts including stabbing Van in a dark alley, shooting him in a drive-by shooting, and sniping him, all of which failed. The latest attempt was conducted by Henry Trent, who had been trained by the backers. He was also outsmarted by Van, who sent Sophia to kill Trent and his men. This she did, though Trent triggered a bomb as he died, also killing Sophia.
Little in detail is known about the backers. They are mentioned as having trained Henry Trent, and of finding Van Helsinki 'useful in the past', but he 'knew too much' now. It is possible that they engineered the Loren Case, or were partly responsible for him being fired, and now do not want him to return to the police force.