Context. The origin of subluminous Type Ia supernovae (SNe Ia) has long eluded any explanation, because all Chandrasekhar-mass models have severe problems reproducing them. Recently, it has been proposed that violent mergers of two white dwarfs of 0.9   M⊙ could lead to subluminous SNe Ia events that resemble 1991bg-like SNe Ia. Aims. Here we investigate whether this scenario still works for mergers of two white dwarfs with a mass ratio below one. We aim to determine the range of mass ratios for which a detonation still forms during the merger, as only those events will lead to an SN Ia. This range is an important ingredient for population synthesis and one decisive point for judging the viability of the scenario. In addition, we perform a resolution study of one of the models. Finally we discuss the connection between violent white dwarf mergers with a primary mass of 0.9   M⊙ and 1991bg-like SNe Ia. Methods. The latest version of the smoothed particle hydrodynamics code Gadget3 was used to evolve binary systems with different mass ratios until they merge. We analyzed the result and looked for hot spots in which detonations can form. Results. We show that mergers of two white dwarfs with a primary white dwarf mass of  ≈ 0.9   M⊙ and a mass ratio more than about 0.8 robustly reach the conditions we require for igniting a detonation and thus produce thermonuclear explosions during the merger itself. We also find that, while our simulations do not yet completely resolve the hot spots, increasing the resolution leads to conditions that are even more likely to ignite detonations. Additionally, we compare the abundance structure of the ejecta of the thermonuclear explosion of two merged white dwarfs with data inferred from observations of a 1991bg-like SN Ia (SN 2005bl). The abundance distributions of intermediate mass and iron group elements in velocity space agree qualitatively, and our model reproduces the lack of material at high velocities inferred from the observations. Conclusions. The violent merger scenario constitutes a robust possibility for two merging white dwarfs to produce a thermonuclear explosion. Mergers with a primary white dwarf mass of  ≈ 0.9   M⊙ are very promising candidates for explaining subluminous SNe Ia. This would imply that subluminous SNe Ia form a distinct class of objects, which are not produced in the standard single white dwarf scenario for SNe Ia, but instead arise from a different progenitor channel and explosion mechanism.