  Regular arrays of magnetic atoms on a superconductor provide a promising
platform for topological superconductivity. In this work we study effects of
disorder in these systems, focusing on vacancies realized by missing magnetic
atoms. We develop approaches that allow treatment of ferromagnetic dense chains
as well as long-range hopping ferromagnetic and helical Shiba chains at
arbitrary subgap energies. Vacancies in magnetic chains play an analogous role
to magnetic impurities in a clean $s$-wave superconductor. A single vacancy in
a topological chain gives rise to a low-lying "anti-Shiba" state below the band
edge of a regular magnetic chain. Proliferation of the anti-Shiba band formed
by a finite density of hybridized vacancy states leads to deterioration of the
topological phase, which exhibits unusual fragility in a particular parameter
region in dilute chains. We also consider local fluctuation in the Shiba
coupling and discuss how vacancy states could contribute to experimental
verification of topological superconductivity.
