G'day freekngeek,

I think this is probably the algorithm you're after but see notes at the end.

#!/usr/bin/env perl

use strict;
use warnings;

my $in_plus_lines = 0;

while (<DATA>) {
    chomp;

    if (/^\+(.*)$/) {
        print "\n" unless $in_plus_lines;
        $in_plus_lines = 1;
        print $1;
    }
    else {
        $in_plus_lines = 0;
        print "\n" if $. > 1;
        print "$_";
    }
}

print "\n";

__DATA__
* asterisk_line_1
*
.dot_line
+ plus_line_1
+ plus_line_2
* asterisk_line_3
+ plus_line_3
+ plus_line_4
* asterisk_line_4
+ plus_line_5
+ plus_line_6
plain_text_line_1
+ plus_line_7
plain_text_line_2
+ plus_line_8
*
*asterisk_line_6
*asterisk_line_7
plain_text_line_3
[download]

Output:

$ pm_cat_plus_lines.pl
* asterisk_line_1
*
.dot_line
 plus_line_1 plus_line_2
* asterisk_line_3
 plus_line_3 plus_line_4
* asterisk_line_4
 plus_line_5 plus_line_6
plain_text_line_1
 plus_line_7
plain_text_line_2
 plus_line_8
*
*asterisk_line_6
*asterisk_line_7
plain_text_line_3
[download]

Notes:

• Your sample input data could be substantially reduced: quite a few lines at the beginning and end could be removed; the length of lines could also be reduced as they can become hard to read when concatenated (due to wrapping).
• Expected output would have been useful. I don't believe your prosaic description of the wanted output is correct; e.g. "I want all the lines to be in one line which start with '+' sign" doesn't look right — I think you want groups of lines starting with '+', not all lines.
• The differences in data in consecutive lines is hard to discern, e.g. it takes a fair amount of effort to tell "PC_M1_M2_75_500_75_500_75_500_75_500_75_bot" and "PC_M1_M2_75_100_75_100_75_100_75_100_75_bot" apart.
• According to "and then removes the '+' sign", you end up with a leading space when the "+" lines are concatenated. Is that what you wanted? (Expected output would have made that obvious.)

As you can see, I've used completely different input; hopefully, the output is easier to read. Given the points above, my algorithm may be incorrect: there may be enough for you to correct it for your needs; if not, please address those points before asking follow-up questions.