Angle-resolved photoemission data taken on some Bi2Sr2CaCu2O8+y single crystals exhibit the formation of a superconducting gap in the absence of a quasiparticle normal state band. We observe the opening of the superconducting gap in the same regions of the Brillouin zone for which it is observed for samples that do exhibit a quasiparticle normal state. The absence of a dispersing quasiparticle normal state indicates that the normal state electronic states in these samples are almost localized in real space. Our data suggest that two types of carriers can coexist, and contribute to forming a superconducting gap, in these materials.