The gemara says that R. Yehuda and R. Akiva argue whether there is malkus for a la'av sh'ein bo ma'aseh. We pasken like R. Akiva that there is no malkus for a la'av that doesn't require an action. The gemara considers both motzi shem rah and eidim zomimin to be a l'av she'ein bo ma'aseh. However, the Aruch La'ner discusses what the halacha is if a person would be motzi shem rah against his wife, in writing, without speaking. He concludes that even according to the Rambam who holds that a witness cannot send his testimony to beis din in writing, if he would actually write it in the presence of the beis din, it would qualify as motzi shem rah. He supports this conclusion with the Node B'Yehuda (kama c.m. 30) who says the same thing, within the context of discussing an oath taken in writing (see also r. akiva eiger who discusses this in a teshuva). Based on this the Aruch La'ner asks a very strong question on the Magid Mishna. The M.M. (Sechirus 13) holds that when we exempt a לאו שאין בו מעשה from malkus, it only includes la'avin that cannot be violated with action, but any la'av that can be violated with action, would receive malkus even if violated passively. Now, since both eidim zomimin and motzi shem rah can be violated with the action of writing, why does the gemara consider them to be לאו שאין בו מעשה? The Aruch Hashulchan himself points out that the sha'ar hamelech (chometz u'matza 1) already rejects the opinion of the magid mishna. He himself limits the suggestion of the magid mishna to the prohibitions where the Torah itself describes an action in the la'av such as "do not muzzle". But, when the description of the l'av in the Torah is passive, one would not receive malkus for a passive violation even if it can be violated actively. Since motzi shem rah is described in the Torah passively, it is a לאו שאין בו מעשה even according to the magid mishna.
After establishing that a לאו שאין בו מעשה that is violated passively doesn't get malkus even if it can be violated actively, we can still ask about prohibitions that are violated with in action, but the actual issur is violated passively. For example, when one swears to eat a loaf of bread and throws it into the ocean, he may have done an act, but his violation is still passive - not eating the loaf of bread (see steipler in shavuos). Tosafos writes that R. Akiva who holds that there is no malkus for a לאו שאין בו מעשה, still holds that there would be malkus for allowing kelayim to exist. Tosafos is forced to say that the malkus for מקיים כלאים בכרם isn't by just having it, rather for building a fence to protect it. It seems from Tosafos that although the actual issur is to be מקיים כלאים, which is by definition passive, when it is violated through an action such as by building a fence, there would be malkus for it.