We discuss the uniruledness of various base loci of linear systems related to the canonical divisor. In particular we prove that the stable base locus of the canonical divisor of a smooth projective variety of general type is covered by rational curves.
"On the uniruledness of stable base loci." J. Differential Geom. 78 (3) 521 - 541, March 2008. https://doi.org/10.4310/jdg/1207834555