If you activate the effect of "Nobleman-Eater Bug" and select 2 monsters, then "Ring of Destruction" is chained and destroys 1 of the selected monsters, you still destroy the remaining monster when "Nobleman-Eater Bug"'s effect resolves.
If "Nobleman-Eater Bug" is the only monster on the field and it is flipped face-up, then it destroys itself with its effect.
EARTH|
Level 5|[ Insect / Flip / Effect ]
ATK 900|
DEF 1200