How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem?

A few decades ago, Kerker et al. [J. Opt. Soc. Am. 73, 765-767 (1983)] theoretically pointed out the interesting possibility of conceiving small magnetodielectric spheres that may provide zero scattering in the forward direction, despite significantly larger scattering in any other direction. Recent experimental and theoretical papers on the topic have further discussed this possibility in more realistic scenarios. Inspecting some of their analyses, it seems indeed possible to conceive nanoparticles characterized by a scattering pattern with a sharp minimum, although not zero, in the forward direction. From a theoretical standpoint, however, it is well known that the total scattered power from any object has to be proportional to a portion of the scattered field in the forward direction, implying that very small or zero forward scattering should be synonymous to even smaller or zero total scattering, regardless of the nature of the object and of its design. Using analytical theory and an accurate scattering formulation, we clarify the nature of this apparent paradox and the limitations of this anomalous phenomenon in terms of particle size. In this way, we shed some new light on theoretical and experimental papers on the topic, identifying relevant missteps in some of their physical interpretation, and considering the general possibility of verifying these effects. This discussion may also be relevant to some cloaking applications using exotic artificial materials.