That allows arbitrary insertions anywhere in the string, so "silly gamma" would match "sigma". The requirement
"sigma" matches "sig<SOMETHING>ma"
can also be read as allowing for only a single insertion. That looks simpler, but the regex is harder to build. Here is one way: 
my $word = 'sigma';

my $re = join '|' =>
    map join( '.*?' => map quotemeta,  @$_) =>
    map [ substr( $word, 0, $_), substr( $word, $_)] =>
    1 .. length( $word) - 1;

foreach my $text (
   'sigma',
   'stigma',
   'silly gamma',
   'magma',
) {
   print("$text ", ($text =~ $re ? "matches" : "doesn't match"), "\n")
+;
}

[download]
It involves splitting $word in all pairs of non-empty substrings, something that comes up occasionally. I have yet to find a satisfactory solution for that. Using substr() like I did above is clear enough, but lengthy. 
map { [ $word =~ /(.{$_})(.*)/] } 1 .. length( $word) - 1;

[download]
is shorter but less readable.

What else?

Update: No improvement either way, but fun: 

map { ++ pos; [ split /\G/] } ( $word) x ( length( $word) - 1);

[download]

Anno

In reply to Re^2: matching with inclusion by Anno
in thread matching with inclusion by vitaly

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