  This paper is concerned with two themes: imprisoned curves and the b-length
functional. In an earlier paper by the author, it was claimed that an endless
incomplete curve partially imprisoned in a compact set admits an endless null
geodesic cluster curve. Unfortunately, the proof was flawed. We give an outline
of the problem and remedy the situation by providing a proof by different
methods. Next, we obtain some results concerning the structure of b-length
neighbourhoods, which gives a clue to how the geometry of a spacetime is
encoded in the pseudo-orthonormal frame bundle equipped with the b-metric. We
also show that a previous result by the author, proving total degeneracy of a
b-boundary fibre in some cases, does not apply to imprisoned curves. Finally,
we correct some results in the literature linking the b-lengths of general
curves in the frame bundle with the b-length of the corresponding horizontal
curves.
