All Parovichenko spaces may be soft-Parovichenko

It is shown that, assuming the Continuum Hypothesis, compact Hausdorff space of weight at most $\mathfrak{c}$ is a remainder in a soft compactification of $\mathbb{N}$. We also exhibit an example of a compact space of weight ${\mathrm{\aleph }}_1$ – hence a remainder in some compactification of $\mathbb{N}$ – for which it is consistent that is not the remainder in a soft compactification of $\mathbb{N}$.