Type Ia supernovae (SNe Ia) come in a large range of luminosities, as determined mostly by the amount of 56Ni produced in the explosion. Nevertheless, they can be normalized and used as standard candles, which suggests that they share a similar origin. The thermonuclear explosion of a Chandrasekhar-mass (MCh) white dwarf accreting mass from a main sequence or red giant companion (the single degenerate scenario) is a favourite configuration, but the presence of SNe Ia that result from the merging of two white dwarfs of total mass exceeding MCh is supported by rate studies. SNe of the spectroscopically peculiar 1991bg class are the least luminous SNe Ia. They produce ∼0.1 M⊙ of 56Ni, which is difficult to reconcile with hydrodynamic explosion models. Here, the properties of the inner ejecta of SN 1991bg are investigated by means of synthetic nebular spectroscopy. In order to reproduce the transformation of the spectra from broader, [Fe ii]+[Fe iii] lines at day ∼120 to narrow, [Fe iii] lines at day ≳210, the innermost region must deviate significantly in density from the prediction of MCh models. In particular, a substantially lower density is required in the innermost ≈3000 km s−1 in order to provide the needed increase of ionization with time. This leads to a mass deficit of ∼0.15 M⊙ in the region inside ≈3000 km s−1 with respect to MCh models, and points to a different type of explosion. Early-time studies require a low explosion kinetic energy and lack of burning products in the outer layers. When combined with the results from this paper, the merger scenario may be a viable candidate for 1991bg-like SNe.