Final answer:
The term for when the posterior background rhythm does not attenuate with eye opening is called banal rhythm or nonreactive EEG. This is abnormal and may indicate underlying neurological conditions.
Step-by-step explanation:
When the posterior background rhythm does not attenuate with eye opening, it is referred to as banal rhythm or nonreactive EEG. The typical reactivity seen is the slowing or reduction of the alpha rhythm in the occipital region when a subject opens their eyes because visual processing disrupts the idle rhythm of the brain. A nonreactive EEG, where this attenuation does not occur, can be indicative of various neurological conditions or states of impaired consciousness.