Can the maker of a Horcrux affect its behavior?

Question

Do Horcruxes negatively affect anyone who comes into contact with them, excluding the owner, or would they have no unhealthy effect on someone the owner considers to be an ally? Does the maker of the Horcrux influence the way it interacts with its surroundings to a certain degree, even if it's non-living? If so, to what degree? For example, if Voldemort had known about the situation his diary was in, could he have dictated how it responded to people who wrote in it?

Answer 1

Voldemort probably cannot control his Horcruxes

“Does Voldemort know when a Horcrux is destroyed, sir? Can he feel it?” Harry asked, ignoring the portraits.

“A very interesting question, Harry. I believe not. I believe that Voldemort is now so immersed in evil, and these crucial parts of himself have been detached for so long, he does not feel as we do. Perhaps, at the point of death, he might be aware of his loss...but he was not aware, for instance, that the diary had been destroyed until he forced the truth out of Lucius Malfoy. When Voldemort discovered that the diary had been mutilated and robbed of all its powers, I am told that his anger was terrible to behold.”

—Harry Potter and the Half-Blood Prince

Voldemort seems to lack sufficient connection to his (inanimate) Horcruxes to even feel when they are destroyed. Dumbledore described these portions of Voldemort's soul as "detached." If Voldemort is so separate from these pieces of himself that he does not know when he has been diminished, it seems unlikely that he can control them from afar. Certainly he would not be able to see what the diary was up to, or know its location.

Indeed, Voldemort was utterly blindsided by the destruction of the non-diary Horcruxes:

But surely if the boy had destroyed any of his Horcruxes, he, Lord Voldemort, would have known, would have felt it? He, the greatest wizard of them all; he, the most powerful; he, the killer of Dumbledore and of how many other worthless, nameless men. How could Lord Voldemort not have known, if he, himself, most important and precious, had been attacked, mutilated?

—Harry Potter and the Deathly Hallows

It thus seems unlikely that he could perceive what was happening around a Horcrux, let alone control it. The fact that he had to check the hiding places of his Horcruxes also suggests he cannot consciously reach out to a Horcrux. The Horcruxes seemed to operate autonomously. Of course, we cannot be certain.

Possible exception

Of course, in the case of living Horcruxes, such as Harry Potter or Nagini, Voldemort was able to connect with them. He had an unusually strong connection with Nagini, and was of course able to reach into Harry's mind over a distance where eye contact would otherwise have been required. Though these actions undoubtedly required effort on his part, he also possessed an unconscious link with Harry, who would sometimes perceive Voldemort's feelings or even his actions. It's difficult to say why he had a stronger connection to Harry or Nagini than to the pieces of soul his his inanimate Horcruxes. Perhaps it was the presence of a whole, living soul (even if not Voldemort's own) in Harry and Nagini that made them easier to reach out to, as opposed to the small, mutilated fraction housed in the non-living Horcruxes.

It also may be that someone less evil, or whose soul was less damaged, or who had been separated from their Horcruxes for a shorter period, might have a stronger connection to their Horcruxes, as indicated in Dumbledore's quote above. As such, they might be able to control their Horcruxes. But we don't really know.

However, Horcruxes may recognize allies to a degree

People with an "affinity" for such evil objects may be not be harmed by the portion of soul therein, and may even be aided:

James Farrell: How did Umbridge manage to conjure a Patronus while wearing the locket when Harry wasn't able to?

J.K. Rowling: Because she is a very nasty piece of work. She has an affinity for this horrible object, which would help rather than hinder her.