  Asteroseismology has proven to be an excellent tool to determine not only the
global stellar properties with a good precision but also to infer stellar
structure, dynamics, and evolution for a large sample of Kepler stars. Prior to
the launch of the mission the properties of Kepler targets were inferred from
broadband photometry, leading to the Input Catalog (KIC Brown et al. 2011). The
KIC was later revised in the Kepler Star Properties Catalog (Huber et al.
2014), based on literature values and an asteroseismic analysis of stars which
were unclassified in the KIC. Here we present an asteroseismic analysis of
45,400 stars which were classified as dwarfs in the Kepler Star Properties
Catalog. We found that around 2% of the sample shows acoustic modes in the
typical frequency range that put them in the red-giant category rather than
cool dwarfs. We analyse the asteroseismic properties of these stars, derive
their surface gravities, masses, and radii and present updated effective
temperatures and distances. We show that the sample is significantly fainter
than the previously known oscillating giants in the Kepler field, with the
faintest stars reaching down to a Kepler magnitude, Kp~16. We demonstrate that
404 stars are at distances beyond 5 kpc and that the stars are significantly
less massive than for the original Kepler red-giant sample, consistent with a
population of distant halo giants. A comparison with a galactic population
model shows that up to 40 stars might be genuine halo giants, which would
increase the number of known asteroseismic halo stars by a factor of 4. The
detections presented here will provide a valuable sample for galactic
archeology studies.
