  Under the axiom of He and Rapoport for the stratifications of Shimura
varieties, we explain a result of G\"{o}rtz, He and Nie that the EKOR strata
contained in the basic loci can be described as a disjoint union of
Deligne-Lusztig varieties. In the special case of Siegel modular varieties, we
compare their descriptions to that of G\"{o}rtz and Yu for the supersingular
Kottwitz-Rapoport strata and to the descriptions of Harashita, Hoeve for the
supersingular Ekedahl-Oort strata.
