In English, calling someone or something 'degenerate' is a major insult. In means that x is not really human or what it seems or what it was. I remember being initially startled or puzzled at the mathematical usage, but it actually is similar, just without the strong insult. A line is a degenerate parabola; a line segment is a degenerate ellipse; crossed lines constitute a degenerate hyperbola; a line segment and a point on the segment constitute a degenerate triangle. There are all limit cases, but they are simplified 'degenerated' limit cases that lack the curvature or dimensionality of the members of the sets that they are limits of. Note that straight lines are only degenerate as a limit of parabolas; they are fine figures in their only right.

0/0 as the limit of 0/x for small x is degenerate in that it looses the essential property of being a well defined real number.

'Degenerate' should not be casually applied to limits, edge cases, corner cases, or oddball cases in general. One could claim that empty counts and collections, including sequences, are 'degenerate' limits in that they loose the 'essential' property of somethingness. But if one means that, then they should be denied existence, as was done for 0 and empty sets, or put in separate classes. (For 0 and {}, there really is a sense of insult that does not apply to lines. We still see it with 'imaginary' numbers.) By including 0 and empty collections in their respective classes, Python denies that they are degenerate. So I do not think any slice should be called 'degenerate'. Certainly, the contrast between all slices working and only some indexes working has nothing to do with 'degeneracy'.