The process by which a virus causes the death of daughter cells which do not contain its genes after host cell division, by a mechanism of post-segregational killing (PSK). The extrachromosomal viral DNA consist of two genes; the product of the second is long lived and toxic, while the product of the first is short lived and antagonizes the lethal action of the toxin. Daughter cells that do not contain the viral extrachromosomal element are killed by the long lived toxin, while daughter cells that do contain the viral extrachromosomal element are protected by the action of the short lived antitoxin it encodes.