That would be my thought as well, or a stably upregulated transcription factor (which would probably be epigenetically upregulated itself). There's a protein complex involved in mediating the interferon response that I've been very interested in--ISGF3 (containing STAT1, STAT2, and IRF9). It's been shown to be upregulated long term in multiple cell lines and primary tissue (
link) and has transcriptional activity even without active interferon signaling. Leads to a stronger ISG response upon stimulation.
Currently unknown what exactly causes it to be upregulated in those cases, but the consistent observation in different contexts means that there is probably some accessible "switch" within all cells.
CD38 wasn't specifically assessed in the study I linked, but its a canonical target of STAT1/this complex.