You should be able to double fork(), then dissociate the new child from the process group, then exec the other program from that grandchild.

POSIX::setsid() is your friend. POSIX is a core module, too, so its use is not subject to installation issues. Use it like this:

#!/usr/bin/perl -w
use strict;
use POSIX qw{setsid};
### or just 'use POSIX;' if you plan to use other
### functions from it, of course

if ( fork ) {
    {
        ### grandparent code goes here
        print "My grandkid should do a cute l'il ls...\n";
    } 
    exit; ### die if we're the parent
}
if ( fork ) {
    exit; ### die if we're the parent of this one, too.
}
### grandchild code starts here
POSIX::setsid; ### should be part of a new session now
exec '/bin/ls', '.';
[download]

The above program should show a proud grandparent bragging about what its grandkid is doing. The grandchild then sticks around after the grandparent is dead. Use a loop in the grandchild if you need to prove it to yourself. The grandparent can also do whatever you want it to do, too.

Update:By all means, also close the standard file handles and chdir to the root directory as edebill suggests. I was overlooking this as assumed for serious background tasks, but I should learn sooner or later that my assumptions are not necessarily those of another monk reading my nodes.