We show that a star orbiting close enough to an adiabatically grown supermassive black hole can capture a large number of weakly interacting massive particles (WIMPs) during its lifetime. WIMP annihilation energy release in low- to medium-mass stars is comparable with or even exceeds the luminosity of such stars due to thermonuclear burning. The excessive energy release in the stellar core may result in an evolution scenario different from what is expected for a regular star. The model thus predicts the existence of unusual stars within the central parsec of galactic nuclei. If found, such stars would provide evidence for the existence of particle dark matter. The excess luminosity of such stars attributed to WIMP ''burning'' can be used to infer the local WIMP matter density. A white dwarf with a highly eccentric orbit around the central black hole may exhibit variations in brightness correlated with the orbital phase. On the other hand, white dwarfs shown to lack such orbital brightness variations can be used to provide constraints on WIMP matter density, WIMP-nucleus scattering and pair annihilation cross sections.