We present the most recent searches for new states with masses below the electroweak scale, based on the full data set collected at or close to the Upsilon(4S) resonance peak by the BABAR detector at the PEP-II e+e- collider. They include, in particular, a search for B-meson decays of the the kind B -> psi_DM + Baryon, where psi_DM is a dark-matter candidate and the baryon can be a proton, a Lambda or a Lambda_c. These decays produce the dark matter particle and baryogenesis simultaneously. Stringent upper limits on the decay branching fraction are derived in the energy region between 0.5 and 4.2 GeV/c^2. We present also a model independent search for an additional Heavy, mostly sterile, Neutral Lepton (HNL) which is capable of mixing with the Standard Model tau neutrino. HNLs are hypothetical particles predicted by many beyond Standard Model theories. HNLs can explain oscillation anomalies as well as the baryon asymmetry in the universe through leptogenesis, and can also provide dark matter candidates. A kinematic approach is taken and no assumptions are made regarding the model behind the origins of the HNL, its lifetime or decay modes. A binned likelihood technique is utilized to scan a HNLs mass-range between 100 and 1300 MeV/c^2. Improved upper limits are presented across this mass range, with more stringent limits being placed at higher masses.