I will demo a "classic way", non-Perl specific way to do this.

You actually have the easiest record parsing case...there is an easily identifiable line that starts a new record and an easily identifiable line that signals the end of the record. This is easier than situations where there is no <EOR> "end of record" and the end of a record is signaled by the start of a new different record.

I used the Perl DATA file handle below, but made a my $fh variable out of it so that filehandle could be passed to a subroutine.
In this algorithm pattern, you loop until you see a start-of-record, then call a subroutine to process that record. The sub returns to the caller and the search for another start-of-record commences.

#!/usr/bin/perl
use strict;
use warnings;

# create a "my $fh data handle" from DATA
# in your code, you would open my $fh to an actual
# input file

my $fh =\*DATA;

while (my $line = <$fh>)
{
    process_record ($fh, $line) if ($line =~ /^zone /);
}

sub process_record
{
    my ($fh, $line) = @_;
    my ($filename) = $line =~ /^zone\s+(\w+)/;
    
    # open a new output file handle to $filename
    print "would print to a file called $filename\n";
    
    my $record_line;
    
    while (defined($record_line =<$fh>) and $record_line !~ /endoffile
+/)
    {
        print "   $record_line";  #you print to outfile
                                  #instead of to STDOUT
    }
    
    # optional close of the output file  
    # closes automatically when its $outfh goes out of scope
}

=prints
would print to a file called 2file2
   record1a
   record1b
   record1c
   record    1d    2
   record    empty
=cut   


__DATA__

#comment line => perhaps a version number?

one 1file1.nest.  1ss
record1a
record1b
record1c
record    1d    2
record    empty
endoffile

zone 2file2.egg.  1ss
record1a
record1b
record1c
record    1d    2
record    empty
endoffile
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