Superconducting 4Hb-TaS2 exhibits unusual phenomena. The Muon spin relaxation rate is enhanced below Tc indicating some change of the local static magnetization in the superconducting state. The low-temperature specific heat is linear-in-T albeit a very sharp superconducting transition, which shape actually fits best to a fully gapped state. Finally, scanning SQUID measurements find a finite vortex density in samples that are cooled at zero field under special conditions. I will present theoretical work we have done to try and explain some of these phenomena based on pair breaking disorder in multi-gap superconductors.