Massive compact systems at 0.2<z<0.6 are the missing link between the predominantly compact population of massive quiescent galaxies at high redshift and their analogs and relics in the local volume. The evolution in number density of these extreme objects over cosmic time is the crucial constraining factor for the models of massive galaxy assembly. We select a large sample of ~200 intermediate-redshift massive compacts from the Baryon Oscillation Spectroscopic Survey (BOSS) spectroscopy by identifying point-like Sloan Digital Sky Survey photometric sources with spectroscopic signatures of evolved redshifted galaxies. A subset of our targets have publicly available high-resolution ground-based images that we use to augment the dynamical and stellar population properties of these systems by their structural parameters. We confirm that all BOSS compact candidates are as compact as their high-redshift massive counterparts and less than half the size of similarly massive systems at z~0. We use the completeness-corrected numbers of BOSS compacts to compute lower limits on their number densities in narrow redshift bins spanning the range of our sample. The abundance of extremely dense quiescent galaxies at 0.2<z<0.6 is in excellent agreement with the number densities of these systems at high redshift. Our lower limits support the models of massive galaxy assembly through a series of minor mergers over the redshift range 0<z<2.