This is a good use for the /e option on the substitution operator.

use strict;
use warnings;

$_ = <DATA>;

if (/<figr n="/) {
  s[<figr n="(\d+)">(.*?)</figr>]
   [qq(<FIGIND NUM="$1" ID="FG.) . sprintf('%03d', $1) . qq(">$2</FIGI
+ND>)]eg;
}

print;

__DATA__
Nerve cells come in many shapes and sizes, but they all have a number 
+of identifiable parts. A typical nerve cell is shown in <figr n="1">F
+igure 1</figr>. Like all other cells in the body, it has a nucleus th
+at contains genetic information.<figr n="2">Figure 2</figr>. The cell
+ is covered by a membrane and is filled with a fluid.
[download]

There is IMHO no sense in the 'if' condition in your snippet :) Or do i miss something?

---

     s;;Just-me-not-h-Ni-m-P-Ni-lm-I-ar-O-Ni;;tr?IerONim-?HAcker ?d;print

Well, it was there (albeit in a more complex form) in the original code, so I thought I'd simplify it but leave it there.

If there's a lot of text and substitutions are only carried out on a small number of lines, then it's probably worth doing a simple check like this - but I'd almost certainly leave it out if I was writing this code from scratch.

As in all cases, the only sure way to know if it's useful is to benchmark the options with something similar to the real data.

--
<http://dave.org.uk>

"The first rule of Perl club is you do not talk about Perl club."
-- Chip Salzenberg

davorg provided you with a working solution, let me explain shortly why your code is not working.

Paraphrasing your code into pseudo-code:

if pattern matches
   set variable $fno   based on above pattern match
   set variable $figno based on above pattern match
   substitute pattern with string that uses $fno and $figno
[download]

There is nothing wrong with your patterns, both work just fine - with the usual caveat about parsing such markup with regexes ...

Generally using regexen for parsing markup is tricky and best left to modules such as HTML::TreeParser. If you can absolutely predict what the markup will be then you may get away with the following:

use warnings;
use strict;

my $str = <<TXT;
Nerve cells come in many shapes and sizes, but they all have a number 
+of
identifiable parts. A typical nerve cell is shown in <figr n="1">Figur
+e
1</figr>. Like all other cells in the body, it has a nucleus that cont
+ains
genetic information.<figr n="2">Figure 2</figr>. The cell is covered b
+y a
membrane and is filled with a fluid.
TXT

$str =~ s/
            <figr\sn="(\d+?)"> # tag including figure number
            (.*?)              # element contents
            <\/figr>           # close tag
        /
            "<FIGIND NUM=\"$1\" ID=\"FG." . # replacement tag
            sprintf("%03d", $1) .           # padded number
            "\">$2<\/FIGIND>"               # remainder of element
        /gmsxe; # Global, multi-line, ignore newline, ignore whitespac
+e, evaluate
print $str;
[download]

Prints:

Nerve cells come in many shapes and sizes, but they all have a number 
+of
identifiable parts. A typical nerve cell is shown in <FIGIND NUM="1" I
+D="FG.001">Figure
1</FIGIND>. Like all other cells in the body, it has a nucleus that co
+ntains
genetic information.<FIGIND NUM="2" ID="FG.002">Figure 2</FIGIND>. The
+ cell is covered by a
membrane and is filled with a fluid.
[download]

If we care about the variations of the input data, even your regex is not enough—e.g it won't match <figr  n="2">Figure 2</figr>, as it contains more than one space between figr and n. The IMHO best solution is to process XML-like data as XML. But the input string can be not well-formed...

I wrote a simple example of how the job could be done, if the input data is a part a of well-formed XML document:

#!/usr/bin/perl

use warnings;
use strict;
use XML::Twig;

my $twig = XML::Twig->new(
    twig_handlers => {
        figr => sub {
            my $fnum = $_->att('n');
            $_->del_att('n');
            $_->set_tag('FIGIND');
            $_->set_att(NUM => $fnum, ID => sprintf('FG.%03d', $fnum))
+;
        }
    }
);

my $str;
{
local $/ = undef;
$str = <DATA>;
}
$str = "<dummy>$str</dummy>";
$twig->parse($str);
$str = $twig->sprint;
$str =~ s!</?dummy>!!g;
print $str;

__DATA__
Nerve cells come in many shapes and sizes,
but they all have a number of identifiable parts. 
A typical nerve cell is shown in <figr n="1">Figure
1</figr>. Like all other cells in the body, 
it has a nucleus that contains genetic information.
<figr  n="2">Figure 2</figr>. The cell is covered by a 
membrane and is filled with a fluid.
[download]

It prints:

Nerve cells come in many shapes and sizes,
but they all have a number of identifiable parts.
A typical nerve cell is shown in <FIGIND ID="FG.001" NUM="1">Figure
1</FIGIND>. Like all other cells in the body,
it has a nucleus that contains genetic information.
<FIGIND ID="FG.002" NUM="2">Figure 2</FIGIND>. The cell is covered by 
+a
membrane and is filled with a fluid.
[download]

---

     s;;Just-me-not-h-Ni-m-P-Ni-lm-I-ar-O-Ni;;tr?IerONim-?HAcker ?d;print

$_ =~ s/<figr n="(.+?)">(.*?)<\/figr>/<FIGIND NUM="$fno" ID="FG.$figno
+">$2<\/FIGIND>/g;
[download]

   $_ =~ s/<figr n="($fno)">(.*?)<\/figr>/<FIGIND NUM="$fno" ID="FG.$f
+igno">$2<\/FIGIND>/g;
[download]

Works is good, but there are better ways. For those, see previous posts.

s{<figr n="([^"]+)">(.*?)</figr>}
{'<FIGIND NUM="'.$1.'" ID="FG.'.sprintf("%03d", $1).'">'.$2.'</FIGIND>
+'}eg;
[download]

my $s = "<foo>stuff</foo>";
#$s =~ s/<foo>(.*?)<\/foo>/<bar>$1<\/bar>/;
$s  =~ s#<foo>(.*?)</foo>#<bar>$1</bar>#;
print $s;
[download]