The environment of NGC 1052 has recently attracted much attention because of the presence of low-surface-brightness galaxies (LSBGs) with apparently "exotic" properties, making it a region of high interest for the detection of new objects. We used public deep photometric data from the Dark Energy Camera Legacy Survey to carry out a comprehensive search for LSBGs over a wide region of 6 × 6 degrees, equivalent to 2 × 2 Mpc at the distance of NGC 1052. We detected 42 LSBGs with reff > 5 arcsec and μg(0) > 24 mag arcsec−2, of which 20 are previously undetected objects. Among all the newly detected objects, RCP 32 stands out with extreme properties: reff = 23.0 arcsec and ⟨μg⟩eff = 28.6 mag arcsec−2. This makes RCP 32 one of the lowest surface brightness galaxies ever detected through integrated photometry, located at just 10 arcmin from the extensively studied NGC 1052-DF2. We explored the presence of globular clusters (GCs) in the LSBGs. We marginally detected a GC system in RCP 32, and argue that this LSBG is of great interest for follow-up observations given its extremely low baryon density. After analyzing the distribution of galaxies with available spectroscopy, we identified a large-scale structure of approximately 1 Mpc that is well isolated in redshift space and centered on NGC 1052. The spatial correlation analysis between the LSBGs and this large-scale structure suggests their association. However, when exploring the distribution of effective radius, we find an overpopulation of large LSBGs (reff > 15 arcsec) located close to the line of sight of NGC 1052. We argue that this is suggestive of a substructure with similar radial velocity in sight projection, but at a closer distance, to which some of these apparently larger LSBGs could be associated. However. possible effects derived from tidal interactions are worthy of further study. Our work expands the catalog of LSBGs with new interesting objects and provides a detailed environmental context for the study of LSBGs in this region.