> The key question is - how to make Bird announcing 0/0 for OSPF ALWAYS? 

Create a static, low-preference „Unreachable“ route for 0/0. If there’s a 
„real“ (functioning) route it’ll override this one and otherwise „unreachable“ 
is always there („reachable“ … [sic]) so you *always* have a 0/0 in your system.

        Clemens


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