Do you see any other signs of significant mods? Non stock MAF, deleted EGR, different injectors etc. Along with testing to see if something has been turned off in the tune, as suggested by another member, connect a scan tool to see if emissions items are deleted when the scan tool is plugged in.
On my tune everything shows up in the scan tool although the EGR is set up so it doesn't throw a CEL. Even though my truck makes pretty good power, everything else, emissions wise, is still turned on in the tune so disconnecting the O2 sensor would still throw a code although I don't have Cats but do use MIL eliminators. Still it is something you could try, just don't rely on only that if it does throw a code.