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Asteroseismology has proven to be an excellent tool to determine not only theglobal stellar properties with a good precision but also to infer stellarstructure, dynamics, and evolution for a large sample of Kepler stars. Prior tothe launch of the mission the properties of Kepler targets were inferred frombroadband photometry, leading to the Input Catalog (KIC Brown et al. 2011). TheKIC was later revised in the Kepler Star Properties Catalog (Huber et al.2014), based on literature values and an asteroseismic analysis of stars whichwere unclassified in the KIC. Here we present an asteroseismic analysis of45,400 stars which were classified as dwarfs in the Kepler Star PropertiesCatalog. We found that around 2% of the sample shows acoustic modes in thetypical frequency range that put them in the red-giant category rather thancool dwarfs. We analyse the asteroseismic properties of these stars, derivetheir surface gravities, masses, and radii and present updated effectivetemperatures and distances. We show that the sample is significantly fainterthan the previously known oscillating giants in the Kepler field, with thefaintest stars reaching down to a Kepler magnitude, Kp~16. We demonstrate that404 stars are at distances beyond 5 kpc and that the stars are significantlyless massive than for the original Kepler red-giant sample, consistent with apopulation of distant halo giants. A comparison with a galactic populationmodel shows that up to 40 stars might be genuine halo giants, which wouldincrease the number of known asteroseismic halo stars by a factor of 4. Thedetections presented here will provide a valuable sample for galacticarcheology studies.

Probing the deep end of the Milky Way with \emph{Kepler}: Asteroseismic analysis of 854 faint Red Giants misclassified as Cool Dwarfs