Suefluence is that part of a Sue's Aura of Smooth that adversely afflicts canon characters, warping them OOC and by extension causing them to do things that they never would do in canon. It can also have an effect on agents, particularly if they're not expecting it, and has caused agents to turn on each other. For example, the first DIA story involved rescuing an agent who had been shot by his partner, who had taken the Sue's side due to overexposure to Suefluence. It may be possible that Suefluence could turn an agent or canon into a Mary Sue, but in all known incidents, agents have managed to escape complete transformation.
Suefluence is most likely part of what creates the very high risk of insanity every PPC agent faces. Being canon characters themselves, albeit from a different continuum, PPC agents' minds may be warped along with the canon they are investigating. Despite being nowhere near as susceptible to badfic effects as targeted canons are, agents' minds can still be worn down by repeated exposure or snapped all at once upon experiencing an extreme assault on sanity.
A Sue's Suefluence ends if she is killed by PPC agents. Paradoxically, it strengthens if she is killed, or kills herself, in the way she had planned. In one such instance, the Suefluence was strong enough to cause Legolas to commit suicide.