  We study a scenario by which a giant wide tertiary star engulfs and forces a
tight binary system of a white dwarf (WD) and a main sequence (MS) star to
enter a common envelope evolution (CEE) with each other, and then unbinds the
WD-MS common envelope. The WD-MS binary system, now with the WD inside the MS
envelope, does not have sufficient orbital energy to unbind their common
envelope. However, as they approach the center of the giant star Roche lobe
overflow to the core of the giant star and/or merger of the WD with the core
remove a large fraction of the WD-MS common envelope or all of it. Namely, the
energy source for unbinding the WD-MS tight common envelope is the triple-star
CEE. For that we term this scenario a parasite CEE. Overall, the destruction of
the MS star absorbs energy from the triple-star system, a process that might
lead to WD-core merger during the triple-star CEE. The parasite CEE leaves
behind either one massive WD that in some cases might explode as a peculiar
type Ia supernova or two close WDs that at later time might explode as a type
Ia supernova. We very crudely estimate the rate of the parasite CEE to be a
fraction of about 0.001 out of all evolved triple stars.
