Is it possible to configure a DNS nameserver so that when performing a
domain name resolution instead of returning the IP address of the
nameserver authoritative for the corresponding child zone, it would
return its domain name. For example, is it possible to have a NS
record in a DNS resolution table
(e.g. US. NS A.GTLD.BIZ.)
without a corresponding A record and simply get A.GTLD.BIZ domain
name when resolving us. domain?

The reason for this question is to figure out whether it's possible to
have a name resolution system that would be an overlay to the existing
DNS and could be deployed using standard DNS software?

Sergei