The Cliff: A Metal-Poor Little Red Dot Hosting an Overmassive Black Hole at $z = 3.55$

JWST has revealed a large population of massive black holes (BHs) in the early Universe with unusual properties which mark them as distinct from low-redshift active galactic nuclei. Such findings have prompted the development of new models of BH formation and growth, and of their co-evolution with host galaxies. Linking the gas-phase metallicity of BH environments to seed masses is key to understanding which evolutionary pathways could explain the population of JWST-discovered BHs. We present new high-resolution JWST NIRSpec/IFU observations covering the rest-frame optical emission lines of a Little Red Dot (LRD) at $z=3.55$, known as The Cliff, from the `Red Unknowns: Bright Infrared Extragalactic Survey' (RUBIES). We find evidence for low metallicity ($Z=0.017\pm0.004 \ Z_\odot$) based on the low narrow-line [OIII]$\lambda5007$/H$\beta$ ratio, supported by the non-detection of low-ionisation emission lines such as [OII]$\lambda\lambda3727,3729$ and [NII]$\lambda\lambda6548,6583$. We find that the observed properties of The Cliff, including its overmassive BH, can be reproduced by some simulations of black hole growth and evolution down to $z\sim3.5$. However, these simulation runs require high seed masses ($10^4 - 10^5\ M_\odot$) and appear as rarely in the simulation volume as in the RUBIES survey volume over redshifts $3<z<4$, highlighting the unusual nature of The Cliff. Future simulations and numerical models will help to uncover how such a metal poor system managed to develop a massive black hole and persist to such low redshift.