Possible to have a subdomain on a different network?

[beparker at yahoo.com]

Situation:

Our company owns a domain, we'll call it "foobartest.com", where we
host a web site for another company.  foobartest.com points directly to
one of the IPs our web server binds to.

The company we host the site for wants a 3rd party to host one little
piece of the site and we link to it, but they want their part to be a
subdomain of foobartest.com, such as 3rdparty.foobartest.com.

Is it possible for the 3rd party, who is a totally different entity and
on a totally different network unrelated to ours, to have a subdomain
of our domain but on their network?

If so, I don't need the dns record setup or anything, I just need to
know if it's possible.

-BEP