We relate the pre-explosion binding energy of the ejecta of core-collapse supernovae (CCSNe) of stars with masses in the lower range of CCSNe and the location of the convection zones in the pre-collapse core of these stars, to explosion properties in the frame of the jittering jets explosion mechanism. Our main conclusion is that in the frame of the jittering jets explosion mechanism the remnant of a pulsar in these low-energy CCSNe has some significance, in that the launching of jets by the newly born neutron star (NS) spins-up the NS and create a pulsar. We crudely estimated the period of the pulsars to be tens of milliseconds in these cases. The convective zones seed perturbations that lead to accretion of stochastic angular momentum that in turn is assumed to launch jittering jets in this explosion mechanism. We calculate the binding energy and the location of the convective zones with the stellar evolution code MESA. For the lowest stellar masses, we study, MZAMS ≃ 8.5–11 M⊙, the binding energy above the convective zones is low, and so is the expected explosion energy in the jittering jets explosion mechanism that works in a negative feedback cycle. The expected mass of the NS remnant is MNS ≈ 1.25–1.6 M⊙, even for these low-energy CCSNe.