The underlying file descriptor itself may be shared

But not even for file descriptors does the sharing extend to the point that opening (or even closing) the FD in one process will cause the same effect on a copy of it in some related process.

The most interesting part of the sharing (to me) is that seek() offsets are shared.

 $ cat kidseek
#!/usr/bin/perl -w
use strict;

$| = 1;
print "One\nTwo\nThree\n";

if( ! fork() ) {
    seek( STDOUT, 4, 0 )
        or  die "Can't seek STDOUT in child: $!\n";
    print "Kid";
    seek( STDOUT, 0, 0 )
        or  die "Can't again seek STDOUT in child: $!\n";
    exit;
}

wait();

print "Dad";
 $ ./kidseek >kidseek.txt
 $ cat kidseek.txt
Dad
Kid
Three
 $
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