Organic cancers arise when an organisms' components malfunction and reproduce excessively. Often they threaten to kill their owners.
Artifacts do not normally behave in this way. They are usually not made up of self-reproducing entities in the first place - and so the chances of their reproduction getting out of control is low.
However there are some classes of cultural phenomena that resemble cancers. Cancers feature out-of control reproduction of cells that are not supposed to reproduce at all, or are time-bombed to only reproduce a limited number of times. Many cultural items have deliberately limited reproductive potential - enforced by technical barriers to copying, legal barriers to copying. Technical barriers include DRM and dongles. However sometimes these barriers are circumvented.
Seen in this light, counterfeiting might be seen as a type of cultural cancer. Hyperinflation caused by excessive money printing could be regarded as being a form of cultural cancer too. Copying material which is supposed to be protected from copying by copyright law is another example. Reproduction of private documents on the internet after a 'doxing' attack could also be regarded as being a form of cultural cancer.
A related phenomena takes place with memetic hitchhiking. Memetic hitchhiking often involves a viral vector with an attached payload. However, if the payload is not securely attached, it can sometimes become detached - leaving the viral content to reproduce is an unrestrained manner, without distributing the payload. The type of mutation that leads to this separation can be damaging. This phenomenon could also be regarded as a form of cultural cancer.
We should also consider defining cancer to refer to cases where part of an organism threatens the integrity of the whole. In this case, another range of scenarios start to look like cultural cancers. Enron was destroyed by rogue elements from within. The Shakers could be seen as having been extinguished by a type of ideological cancer - as could Heaven's Gate.
One problem with classifying these type of phenomena as being cultural cancers is that they don't occur inside proper organisms. Rather, companies and religious groups could be seen as being symbiotic unions of multiple creatures (both cultural and organic) - rather like a Portugese man o' war. Rather than looking like cancer, disorders involving one part of a composite creature profiting at the expense of the whole just look like ordinary resource squabbles within uneasy alliances.