Highly Variable Active Galactic Nuclei in the SRG/eROSITA All-Sky Survey: I. Constructing Sample and Catalog of Sources Detected in Low State

We present the results of our search for highly variable active galactic nuclei (AGNs) the X-ray flux from which changed by more than an order of magnitude during the SRG/eROSITA all-sky survey. Using the eROSITA data obtained in the period from December 2019 to February 2022, we have found 1325 sources the X-ray flux from which in the 0.3-2.3 keV energy band changed by more than a factor of 10 at a confidence level of at least 99.73 %. Of them, 635 objects have been classified as AGNs or AGN candidates. We describe the procedure of searching for highly variable sources and the selection of extragalactic objects among them and describe the statistical properties of the produced catalog. We provide a catalog of 49 sources for which a statistically significant flux in their low state was detected. For the latter we provide their light curves and X-ray spectra and discuss in detail the most interesting of them.