EIGRP has no command to inject a default route into the routing table so there are only two methods by which you can install one into EIGRP:
- Redistribute the default route from another routing source
- Manually summarize a default route to all neighbors
If a static default route is configured without a next hop interface and you configure a network command with 0.0.0.0 IOS will think the route is directly connected and advertise it out to neighbors. However, this will also cause EIGRP to advertise out all directly connected interfaces, this could be a non desirable behavior and as such is never a good idea to advertise the default route in such a way.