The quantum defect is an empirically introduced notion that has allowed convenient interpolations of spectral data along atomic isoelectronic sequences and their extrapolation with respect to the principal quantum number. Both yield valuable spectral information, the latter providing estimates of low-energy-electron elastic scattering phase shifts as well. We examine a recently proposed conjecture concerning the extrapolated value of the quantum defect along an isoelectronic sequence: If the binding energy of the outermost electron vanishes in the singly negative ion, then its asymptotic quantum defect is an integer whose value is equal to the number of occupied shells with the same orbital angular momentum. This behavior is associated with the fact, established by means of appropriate electronic structure calculations, that-asymptotically-the outermost orbital becomes an infinitely diffuse hydrogen-like orbital. In most cases explored the asymptotic behavior can be ascertained by analysis of spectral data along the appropriate isoelectronic sequence, but in some cases the approach to the asymptotic value takes place over a very narrow range of nuclear charge in the vicinity of that of the negative ion.