There are mirror lenses faster than f/8. I can think of several that are f/6.3 (see the Lens Tables sticky in the EF and EF-S Lenses forum in the Equipment section of POTN), and I believe I once saw one that was f/4.
Also, virtually all telescopes, refractive or reflective, may be considered fixed-aperture lenses. Simply take off the eyepiece and put on a T-mount adapter and voilà! Instant camera lens!
There are also other types of fixed-aperture lenses for cameras. None that I'm aware of are worth a damn, however. Most box cameras have fixed-aperture lenses.
The aperture structure has almost nothing to do with the quality of the optics. It's merely a stop mechanism that controls the effective diameter of the objective element.
Fixed focus lenses are another matter entirely. Although I can't think of any real-world examples that have any decent quality, there would be nothing to prevent someone from turning any lens they desire into a fixed-focus lens.
Usually, fixed focus lenses are also fixed aperture or, at the most, two apertures (semi-fixed apertures?). The lens in the classic box camera is such a lens, typically preset to f/16 and pre-focused at the hyperfocal distance. This is how such cameras can take pictures with everything more than a few feet away in focus.
Fancier box cameras sometimes had a switch that changed apertures. When you flipped the switch, you typically got f/8 and lost infinity focus. That was because the hyperfocal distance changed with the aperture, but the lens' focus did not.
