Making use of HI-MaNGA (HI Followup of the Mapping Nearby Galaxies at Apache Point Observatory survey), we construct a sample of unusual neutral hydrogen (HI, 21cm) rich galaxies with low Star Formation Rates (SFRs). We compare this set of 97 galaxies, with two mass-matched control samples: HI rich galaxies with typical SFR and HI non-detected galaxies with low SFR. We investigate the properties of each of these samples, using integral field spectroscopy data from the Sloan Digital Sky Survey IV MaNGA survey and photometry from Wide-field Infrared Survey Explorer (WISE). Using MaNGA data we construct spatially resolved Baldwin-Philips-Terlevich (BPT) ionisation state diagnostic diagrams, and classify the galaxies as either (i) star forming, (ii) composite, (iii) low-ionisation emission-line (LIER), (iv) Seyfert, (v) ambiguous, (or other or not having enough spaxels to classify). We find a high fraction of LIERs in both low SF samples (HI rich; 56%, HI non-detection 47%), very different to the HI rich high SFR sample (14% LIER). We conclude that LIERs are specific to galaxies with low SFR but it is not necessary to have significant HI content. However, HI detected low SFR galaxies are observed to have a greater proportion of central-LIERs (cLIER) compared to HI non-detections which have more extended-LIERS (eLIERs). We make additional comparisons of physical parameters such as velocity dispersion, environment, metallicity, HI rotation, and morphology between our main and control samples to investigate further the reasons why these unusual HI rich galaxies are prevented from forming stars.