Unspecified ... and not relevant, all that failed check is telling us is that he noticed you ... everything beyond that is matter of roleplay interpretation.

Passive perception for starters. And passive perseption is already 10+Perception skill value. So if the opponent managed to go down to 5 with his passive perception he is effectively deaf and blind.
That is once aggain just roleplay interpretation ...
All that number tels us is how hard it will be to slip around him ... he can aswell be just ignorant, distracted, focused on sonething else, or simply sleeping (even if on duty) ... but even as such he cant ignore obvious threat.

Stealth just shouldnt equal "being undetectable by any means" ... and if (and that alone is a HUGE if ... its not even "a" ... its THE huge if ... thats how huge it is) it should mean "being undetectable by any means" ... there simply shouldnt be any check in the first place, since its effectively pointless.