Non-delegated sub-domain problem

Can someone point me in the right direction as to finding information on non-delegated subdomains. In the organization that I work for, we have a weird configuration as a fractal of the company runs their own DNS server, but the server is a subdomain of our domain. At times on their side they get weird resolution issues. Basically, company-xyz.com is us, and they are abc.company-xyz.com. So, when a resolver is pointing to joeschmoe.company-xzy.com, their server forwards to the name server controlling company-xyz.com (us).

The weird problem is, when their forwarding fails (don't know why), the next forward is the internet, which we have a presence as well. But of course, out external doesn't know about our internal name space. Also, their DNS server appends their sub-domain + domain name onto the resolution looking more like this: joeschmoe.company-xyz.com.abc.company-xyz.com. Can someone point me in the direction of finding out if non-delegated subs domains is legal by standard DNS practices?