Finding massive black holes (MBHs, M_BH_~10^4^-10^7^M_{sun}_) in the nuclei of low-mass galaxies (M*<=10^10^M_{sun}_) 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 ~200 UVOIR variability-selected MBHs and significantly detected 17 of them in the deepest available 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. This result reveals the potential for severe biases in occupation fractions derived from data from only one waveband combined with SEDs and scaling relations of more massive black holes and galaxies.