Viññanam anidassanam. This term is nowhere explained in the Canon, although MN 49 mentions that it "does not partake in the allness of the All" — the "All" meaning the six internal and six external sense media (see SN 35.23). In this it differs from the consciousness factor in dependent co-arising, which is defined in terms of the six sense media. Lying outside of time and space, it would also not come under the consciousness-aggregate, which covers all consciousness near and far; past, present, and future. However, the fact that it is outside of time and space — in a dimension where there is no here, there, or in between (Ud 1.10), no coming, no going, or staying (Ud 8.1) — means that it cannot be described as permanent or omnipresent, terms that have meaning only within space and time. The standard description of nibbana after death is, "All that is sensed, not being relished, will grow cold right here." (See MN 140 and Iti 44.) Again, as "all" is defined as the sense media, this raises the question as to whether consciousness without feature is not covered by this "all." However, AN 4.174 warns that any speculation as to whether anything does or doesn't remain after the remainderless stopping of the six sense media is to "objectify non-objectification," which gets in the way of attaining the non-objectified. Thus this is a question that is best put aside.
"Kevatta (Kevaddha) Sutta: To Kevatta" (DN 11), translated from the Pali by Thanissaro Bhikkhu. Access to Insight (Legacy Edition), 30 November 2013, http://www.accesstoinsight.org/tipitaka/dn/dn.11.0.than.html .