ABSTRACT We study a scenario in 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 centre 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 ≈0.001 out of all evolved triple stars.