Barzini would go into hiding. The other three dons (Tattaglia, Cuneo and Stracci) that I consider allies have all just been murdered on the orders of Michael Corleone, who I thought was small potatoes. Not only that, but Michael was able to figure out that his caporegime Tessio and brother-in-law Carlo were working against the family and Michael has had them killed. Barzini would be a fool not to go into hiding.

I suspect that the Barzini Family was still quite strong, however, and there might be another long and destructive war between Barzini and Corleones.