  High-latitude ($|b|>30^{\circ}$) molecular clouds have virial parameters that
exceed 1, but whether these clouds can form stars has not been studied
systematically. Using JCMT SCUBA-2 archival data, we surveyed 70 fields that
target high-latitude Planck galactic cold clumps (HLPCs) to find dense cores
with density of $10^{5}$-$10^{6}$ cm$^{-3}$ and size of $<0.1$ pc. The sample
benefits from both the representativeness of the parent sample and covering
densest clumps at the high column density end ($>1\times10^{21}$ cm$^{-2}$). At
an average noise rms of 15 mJy/beam, we detected Galactic dense cores in only
one field, G6.04+36.77 (L183), while also identifying 12 extragalactic objects
and two young stellar objects. Compared to the low-latitude clumps, dense cores
are scarce in HLPCs. With synthetic observations, the densities of cores are
constrained to be $n_c\lesssim10^5$ cm$^{-3}$, should they exist in HLPCs.
Low-latitude clumps, Taurus clumps, and HLPCs form a sequence where a higher
virial parameter corresponds to a lower dense core detection rate. If HLPCs
were affected by the Local Bubble, the scarcity should favor
turbulence-inhibited rather than supernova-driven star formation. Studies of
the formation mechanism of the L183 molecular cloud are warranted.
