In my answer to How do harmonics work?, I said:
[A] vibrating guitar string has components at many multiples of the base frequency (call it F). To your ear it still sounds like the fundamental, but mathematically it's more like this:
aF + b2F + c*3F + ...
The higher-frequency elements give the note it's timbre; this is how you can tell two instruments apart, or even tell different kinds of guitar strings apart. For example, the sound where
a=1 b=0.6 c=0.3will sound different thana=1 b=0.5 c=0.4. Note that a is always the largest coefficient, since F is the fundamental frequency. If it wasn't it would sound like you were playing a different note, or multiple notes.
That last bit is actually false; I glossed over it for the sake of simplicity. In fact, it's perfectly possible for the fundamental to be weaker than other components of the sound while the perceived note is still that of the fundamental.
By the same logic, it's also possible for a to be so weak that the lowest component is not perceived as the fundamental. In other words, F would not be the fundamental, and I think it would be perfectly accurate to call it a "sub-harmonic" in that case.
It might be difficult if not impossible to create such a sound with a single vibrating string (for example), but you could probably do something like play A440 quietly on one string and A880 loudly on another, and end up with the perceived fundamental at A880 with A440 as your sub-harmonic. Of course, the human ear is quite good and it would also be difficult to prevent the two notes from being perceived distinctly. This might be easier with electronic approaches, as Dr Mayhem talks about.