Quasi-regular singularities are points of incomplete and in-extensible geodesics that spiral infinitely around a topologically closed spatial dimension. These are the weakest form of singularity, in that the Riemann tensor is completely finite in all parallelly propagated orthonormal frames.No observer near a quasi-regular singularity, nor one who falls in to the singularity, feels unbounded tidal forces.
Reference: https://pdfs.semanticscholar.org/3f03/a70f148528e55f9391b6b02d52f86a30f1f9.pdf
Basically, as I understand it, it's a line singularity that has no tidal forces tied to it since it's not produced by curvature. Exactly the same as Dirac strings.(well maybe not exactly the same)