open MODULE, "perldoc -m Session|" or die "Failed to open pipeline($!)
+";

    while (<MODULE>) {
    open(X,"> xxx_dump.txt")|| warn "Fail: ($!)";
    print X $_;

    }
close X;
close S;
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You are opening the file for each line, overwriting the previous output. Open it just once before entering the loop.
لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

Unfortunatelly, still doesn't work. Now, I am getting empty file ;/

my @tab;
    open MODULE, "perldoc -m ModuleX|" or die "Failed to open pipeline
+($!)";
        open(X,"> xxx_dump.txt")|| warn "Fail: ($!)";

    while (<MODULE>) {
    @tab = split;
    foreach $_ (@tab) {
            print X $_;

    }
        }
        close X;

    close MODULE;
[download]

What is wrong ? Maybe perldoc -m ModuleX doesn't work with used modules ?