  Finding massive black holes (MBHs, $M_{BH}\approx10^4-10^7 M_{\odot}$) in the
nuclei of low-mass galaxies ($M_{*}\lessapprox10^{10} M_{\odot}$) is crucial to
constrain seeding and growth of black holes over cosmic time, but it is
particularly challenging due to their low accretion luminosities. Variability
selection via long-term photometric ultraviolet, optical, or infrared (UVOIR)
light curves has proved effective and identifies lower-Eddington ratios
compared to broad and narrow optical spectral lines searches. In the
inefficient accretion regime, X-ray and radio searches are effective, but they
have been limited to small samples. Therefore, differences between selection
techniques have remained uncertain. Here, we present the first large systematic
investigation of the X-ray properties of a sample of known MBH candidates in
dwarf galaxies. We extracted X-ray photometry and spectra of a sample of
$\sim200$ UVOIR variability-selected MBHs and significantly detected 17 of them
in the deepest available \emph{SRG}/eROSITA image, of which four are newly
discovered X-ray sources and two are new secure MBHs. This implies that tens to
hundreds of LSST MBHs will have SRG/eROSITA counterparts, depending on the
seeding model adopted. Surprisingly, the stacked X-ray images of the many
non-detected MBHs are incompatible with standard disk-corona relations, typical
of active galactic nuclei, inferred from both the optical and radio fluxes.
They are instead compatible with the X-ray emission predicted for normal
galaxies. After careful consideration of potential biases, we identified that
this X-ray weakness needs a physical origin. A possibility is that a canonical
X-ray corona might be lacking in the majority of this population of
UVOIR-variability selected low-mass galaxies or that unusual accretion modes
and spectral energy distributions are in place for MBHs in dwarf galaxies.
