In this answer, List of Underlining Packages - Pros and Cons, I modified censor to underline with the text still intact, allowing for line breaks, even breaking the underline for descending letters (but it doesn't handle hyphenation). Most importantly, I added a math underlining/censoring capability.
So I took that solution, and removed the stuff that places the text there, leaving just the underlining. Then by setting \censorruleheight=0ex, the underline is set to zero thickness and so it disappears. So you have \censor for a string of words on a single line, \blackout for a group of words across multiple lines, and \mblackout for math expressions.
This approach does allow for blankspace that spans not only multiple lines, but even page breaks!
\documentclass{article}
\usepackage{censor}
\usepackage{stackengine}
\usepackage{scalerel}
\censorruleheight=0ex
\makeatletter
\long\def\blackout#1{%
\def~{-}%
\protected@edef\save@arg{#1}%
\expandafter\censor@Block\save@arg\stringend\let~\sv@tilde}
\let\sv@cenword\@cenword
\newcommand\m@cenword[1]{\ThisStyle{%
\stackengine{\mcensorruledepth}{$\SavedStyle\phantom{#1}$}%
{\rule{\widthof{$\SavedStyle#1$}}{\the\censorruleheight}}{U}{c}{F}{T}{L}}}
\newcommand\mblackout[2][\dp\strutbox]{%
\let\@cenword\m@cenword%
\def\mcensorruledepth{#1}%
\blackout{{#2}}%
\let\@cenword\sv@cenword%
}
\makeatother
\parskip 1em
\begin{document}
The \verb|\censor| command can blackout \censor{this text} which appears on a single line.
The \verb|\blackout| command allows the censoring of text even if it crosses a line/page boundary.
To test this macro, let's see \blackout{if this block of text is truly blacked out} across a line boundary.
For total blanking, there should be no need for \verb|\xblackout|.
But here is math versions, not black out, then blacked out:
\[ y = A x^2 + Bx + C + D\]
\[ y = \mblackout{A x^2} + Bx + \mblackout{C} + D\]
\[ y = \frac{a^3 + b^2 + c}{d_3} + \frac{a^3 + b^2 + c}{d_3}\]
\[ y = \mblackout{\frac{a^3 + b^2 + c}{d_3}} + \frac{a^3 + b^2 + c}{d_3}\]
\end{document}

\ExplSyntaxOn\ExplSyntaxOffblock, but so far it worked with anything I threw at it. – user1612064 Sep 28 '13 at 21:30