ABSTRACT We study stellar binary evolution that leads to the formation of a white dwarf (WD) that explodes in a thermonuclear supernova at the termination of a common envelope evolution (CEE) shortly before the core of its companion explodes as a core-collapse supernova (CCSN). The CCSN explosion of the core, which is the remnant of a red supergiant (RSG) star, might take place few months to several years after the explosion of the WD as a thermonuclear supernova, i.e. a Type Ia peculiar supernova (peculiar SN Ia). Using the evolutionary code mesa-binary, we simulate the evolution of binary systems with stars of initial masses of $6\!-\!7.5\, {\rm M}_\odot$. The more massive star, the primary, transfers mass to the secondary star and leaves a CO WD remnant. The secondary becomes massive enough to end in a CCSN. As the secondary evolves to the RSG phase, it engulfs the WD and the system experiences a CEE that ends with a WD–core binary system at an orbital separation of af ≃ 1–5 R⊙. Our simulations show that the core explodes as a CCSN at $t_{\rm CEE-CCSN} \simeq 3000 \!-\! 10^5 {~\rm yr}$ after the CEE. We assume that if the WD accretes helium-rich gas from the core it might explode as an SN Ia in the frame of the double detonation scenario for SNe Ia and peculiar SNe Ia. We predict the very rare occurrence of a peculiar SN Ia followed within months to years by a CCSN.