There are screensavers for the Nokia 3310 but my grandma does not use one and it’s still alright. The damage you saw may have happened if the driver hanged and started sending DC to the display instead of AC pulses, which is unlikely for dedicated COB ones like on the 3310 or 7100. That (and mechanical damage such as glass breaking or delamination, or very high voltage, obviously) is the only way an LCD cell itself can degrade. Much more frequently, a rubber strip or flat cable gets loose, or the MCU or LCD driver fails (very common in 1980s/1990s CMOS technology, such as calculators). Therefore, in a well-built device not exposed to shocks and quick temperature changes, an STN LCD will be unlikely to fail before anything else.