M dwarfs are the most common type of star in the galaxy (~70%) and the type of star with the highest frequency of short-period, terrestrial planets, with a trend of increasing planet occurrence with decreasing stellar mass down to ~M5 type dwarfs. Whether this trend continues for later-type M dwarfs is not well understood. Recent literature suggests that a flat rate may continue beyond M5, while recent models suggest that terrestrial planet occurrence should drop off for the lowest-mass stars. At the same time, two well-known late-type M dwarf systems with multiple terrestrial planets exist (TRAPPIST-1 and Teegarden’s Star), which also notably exhibit indicators of low surface gravity despite tracers for field age. To investigate this, we use a volume-limited sample of low-resolution spectra from NASA IRTF/SpeX of nearby (within 30 pc) ultracool dwarfs (UCDs; spectral types later than M5) to characterize their spectral types and gravity classes. We then analyze their TESS lightcurves to investigate a potential link between spectral indicators of low surface gravity and terrestrial planet occurrence. We calculate the occurrence rate for low-gravity UCDs and compare it to a derived upper limit on the possible terrestrial planet yield for field-type UCDs. We find that the occurrence rate of terrestrial planets is significantly higher for low-gravity UCDs than for field-type UCDs. This may hint at spectral indicators of star-planet interactions that can be used to prioritize future targets for follow-up with next-generation ground- and space-based telescopes. We highlight the need for even larger samples and increased sensitivity to terrestrial planets around UCDs to enable further insight into the cause of this low-gravity signature and more robust comparisons to planet-formation models. These results have important implications for understanding planet formation, system evolution, and star-planet interactions around the lowest-mass stars.