I think the hypothetical is certainly possible. There is a whole line of CAFC cases including the recent Lizardtech v. Earth Resources Mapping which we've discussed here before that suggest that a disclosure can fail to support a broad claim by describing only a single embodiment or describing a single way of implementing a given feature.
I thought there was a case directly on point that came down within the last 6-18 mos. that said more or less the opposite. The losing argument of the defendant was that they didn't enable our embodiment therefore we don't infringe or the claim's invalid. The holding was that enabling one embodiment, any embodiment, was all that's required to enable a claim. Sorry, don't remember the exact case off the top of my head.
Now, I've heard of specifics of a described embodiment being imported into the claim, but that's a matter of claim interpretation, not sufficiency of enablement.
I think the only way that the hypothetical could be possible would be in the best mode requirement. If the specific species has a different best mode than the broad genus and the former best mode was included but the latter best mode omitted, then I suppose it's possible for the broad genus to fail S.112 par. 1 while the narrower species would pass muster.
Perhaps I'm dense, but I don't see how one could enable -- as an example -- an orange without also enabling citrus or even generally spherically shaped fruit. The law is quite clear that you don't have to enable each and every possible embodiment of a claimed invention, just one.
Regards.
P.S. Should have done this before posting, but I just looked up and skimmed the case. I think it's an unfortunate decision. The law as I now understand it is that enablement of just one embodiment is sufficient, unless it's not. Great.
The odd circumstance here was that a narrower claim had the same limitation that the court wanted to import into the claim, so the doctrine of claim differentiation impeded that. In effect, it didn't matter which of two alternatives the court chose: ignore the doctrine of claim differentiation and allow claims 1 and 21 to be identical and valid, or disallow importation of the limitation into claim 21 and invalidate claim 21, allowing the otherwise identical claim 1 stand. The effective result would have been the same either way.