The solution you added in the update doesn't work.

$string =~ s/(_)[^']/$1'/g;
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should be

$string =~ s/(_)([^'])/$1'$2/g;
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That can also be written as

$string =~ s/(_)(?=[^'])/$1'/g;
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and

$string =~ s/_\K(?=[^'])/'/g;    # 5.10+
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