Hi, thanks for posting your code.

Here is a version that appears to do what you want. Note the following things:

• You need to chomp() the user input to remove the newline so you can use the string in a comparison.
• The sample data you provided doesn't contain anything that would match your first regexp.
• The regexp for matching the start of the line with the user input crudely and *only* matches negative numbers with exactly one integer and one decimal place. You'll need to change it if the user could enter a positive number, or a negative integer, or anything else.
• After capturing the match it is available in the special variable $1, which is used for the comparison.
• I placed your sample data in the script in the __DATA__ section for this demo; it's fine to open and read a file as in your original. I also skipped the writing to an out file.
• I placed multiple "debug statements" in the code, i.e. printing out things to show what's going on. Once the program is working correctly you can remove those, but it's a good technique for discovering problems in your data processing.

#!/usr/bin/perl 
use strict;
use warnings;
use feature 'say';

print "The lower the score the more stable the structure.", "\n",
      "Please set a limiting value e.g. -3: ", "\n";

chomp( my $value = <STDIN> );
chomp( my @input = <DATA> );
my @trash;
my @treasure;

for ( @input ){
    if ( /^>+/ ) {
        say "$_ matches '/^>+/'";
        push @treasure, $_;
    } elsif ( /^None/ ) {
        say "$_ matches '/^None/'";
        push @trash, $_;
    } elsif( /(^[\d\.-]{4})/ ) {
        say "$_ matches '/(^[\d\.-]{4})/'";
        if ( $1 <= $value ) {
            say "$1 is <= $value";
            push @treasure, $_;
        } else {
            say "$1 is > $value";
            push @trash, $_;
        }
    } else {
        say "$_ doesn't match anything!";
        push @trash, $_;
    }
}

say 'Treasure:';

foreach my $stuff ( @treasure ) {
    say $stuff;
}

__END__
hsa_circ_0067224|chr3:128345575-128345675-|NM_002950|RPN1 FORWARD
-4.4.. 6 .. 17 xxxxxxxxxxGTGAC CAGT ATGC ACTG AAGATGAGGTTTGTG
-0.9.. 5 .. 18 xxxxxxxxxxxGTGA CCAGT ATGC ACTGA AGATGAGGTTTGTGG
None.. 1 .. 20 xxxxxxxxxxxxxxx GTGACCAGTATGCACTGAAG ATGAGGTTTGTGGAC
[download]

Hope this helps!