Practical uses for skips with negative stretch or shrink components

Question

I am currently looking somewhat carefully at how TeX manipulates skips, and I am having trouble finding practical use cases for skips with a negative stretch or shrink component, such as \Askip and \Bskip in the following.

\newskip\Askip
\newskip\Bskip
\Askip 0pt plus -2pt minus 3pt
\Bskip 0pt plus 1fil minus -4bp

They lead to odd situations. For instance, putting a skip with a large negative stretch component in a box that it somewhat underfull will cause other skips to shrink proportionally to their stretch component.

\hbox to 200pt{A B C\hskip 0pt plus -50pt}\bye

What happens is that since the box is underfull, TeX looks at the sum of the available stretch components. Since this sum is negative, the stretch components are multipled by a negative number.

So, obviously this example is not useful, but are there some more useful examples of what negative glue can be used for?

Answer 1

As @egreg mentioned in comments, they are usually paired with equal positive values.

plain and latex both have

 \def\filbreak{\par\vfil\penalty-200\vfilneg}

if the break happens the negative stretch is thrown away at the top of the next page, but if it does not happen, it counteracts the fil space before the penalty leaving zero total stretch.

Answer 2

maybe not exactly what is requested, but an absolute negative skip is useful in creating composite symbols, e.g.

x \rightarrow\mskip-15mu\rightarrow\mskip-15mu\rightarrow y

will give you

it's also instructive to notice that \llap, \rlap, \clap and their vertical friends are all based on \hss or \vss which are primitives defined with infinite negative shrink and stretch. \llap is immensely useful for positioning page numbers flush right in a table of contents. and marginal notes couldn't exist without these facilities.