If the body of the loop is the same, and only the source changes, you can refactor the source instead of the loop body.

Example implementation:

use strict;
use warnings;
use File::Tail;
my %opt = (c => 0);
my $MAILLOG = $ARGV[0];


#
# $reader will hold a reference to an anonymous subroutine that reads 
+from
# a source. Either a filehandle or a File::Tail object.
#
my $reader = undef;

if ($opt{'c'}) {
    my $fh = undef;
    open $fh, "<", $MAILLOG or die "Failed to read $MAILLOG. $!";
    # Create an anonymous subroutine that reads from the lexical $fh
    # filehandle. Once $reader goes out of scope the file will be clos
+ed
    $reader = sub { readline($fh) };
} else {
    my $log = File::Tail->new(
        name => $MAILLOG,
        tail => -1,
        interval => 1,
        max_interval => 1,
    );
    # Create an anonymous subroutine that reads from the $log
    # object. Once $reader goes out of scope the object will be
    # destroyed.
    $reader = sub { $log->read() };
}

while (defined(my $line=$reader->())) {
    print $line;
}
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