We discovered that RX And, one of prototypical Z Camtype dwarf novae, underwent a deep, extended faint state in 1996-1997. Time-resolved photometry at the bottom of the fading revealed the presence of strong flickering, and the absence of detectable orbital modulation. This finding indicates that the mass-transfer remained even at the deepest minimum of the fading, contrary to what was observed in a deep minimum of a VY Scl-type star, MV Lyr. RX And subsequently underwent a brightening (outburst) during its recovery stage. The photometric and spectroscopic characteristics of the brightening significantly differed from those of ordinary outbursts of RX And, and are considered to resemble an inside-out type outburst of a long-period dwarf nova. An examination of historical visual observations revealed the possible presence of ∼10-yr periodicity, which is close to what has been proposed for MV Lyr. The common observed features between RX And and VY Scl-type stars may suggest a common underlying mechanism for producing temporary deep fadings. The departure from the disk instability model, as observed in VY Scl-type stars, was not apparent in the present fading of RX And. In conjunction with the recently published Hubble Space Telescope observation during the same fading, we can conclude that the phenomenological difference from the VY Scl-type fading is understood as a smaller effect of irradiation on the accretion disk in RX And.