The optical outburst spectra of low-mass X-ray binaries enable studies of extreme accretion and ejection phenomena. While some of their spectroscopic features have been analysed in detail, the appearance of broad absorptions in the optical regime has been traditionally neglected. In this work, we introduce the first population study dedicated to these features with the aim of understanding their fundamental properties and discussing them in the context of their origin. We complemented the study with a spectroscopic database of six low-mass X-ray binaries during outburst, in order to assess their evolution. We find that broad absorptions are ubiquitous, with the majority of black hole low-mass X-ray binaries exhibiting them in spite of a typically scarce outburst coverage. Their detection does not depend on the orbital inclination or the compact object nature, but they seem favoured in systems with orbital periods shorter than < 11 h. They predominantly occur in the hydrogen Balmer series, being stronger at shorter wavelengths, and they are detected across all X-ray states. Their profiles are best fitted with a Gaussian distribution of σabs= 1400±500 km s-1 <!--inline-formula id="FI1"> <alternatives> σ abs = 1400 ± 500 km s − 1 <![CDATA[$ \sigma_{\mathrm{abs}}=1400\pm 500\,\mathrm{km\,s}^{-1} $]]> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" id="img_eq1" mime-subtype="gif" mimetype="image" xlink:href="aa58961-26-eq1.gif"/> </alternatives> . They exhibit typical mean centroid velocities close to the systemic velocity, which links them to the accretion disc. Their equivalent widths, with typical values of EWabs = 4±2 Å <!--inline-formula id="FI2"> <alternatives> E W abs = 4 ± 2 Å <![CDATA[$ EW_{\mathrm{abs}}=4\pm 2\,{\AA} $]]> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" id="img_eq2" mime-subtype="gif" mimetype="image" xlink:href="aa58961-26-eq2.gif"/> </alternatives> , slowly evolve over timescales of weeks to months, reaching up to ∼17 Å <!--inline-formula id="FI3"> <alternatives> ∼ 17 Å <![CDATA[$ {\sim}17\,{\AA} $]]> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" id="img_eq3" mime-subtype="gif" mimetype="image" xlink:href="aa58961-26-eq3.gif"/> </alternatives> in the most extreme cases. We find that the normalised depth of these broad absorptions is anti-correlated with the system luminosity, and that they show constant line ratios over the whole sample. Based on these properties, we favour a scenario where BAs arise from a stable, optically thick layer of the accretion disc, below the hotter chromosphere-like region that produces the emission line components. Our study is consistent with the continuous presence of broad absorptions during the whole outburst, with their visibility being conditioned by the emission lines filling the broad absorption profile and veiling by the X-ray reprocessed continuum.