An example of losing the War but willing the peace would be the CSA (Confederate States of America) where they lost the US Civil War but their Racial policies and their Racial Privileges were secured and reinforced during the peace that followed the Civil War the the betray of Reconstitution.
Another example of losing the War but winning the peace would be the Axis Powers who stood for White Global Empire and Fascism lost to the Allied Powers who stood for the same damn thing, they just wanted to employ a different methodology. The Allies later integrated the Nazis into their fight against Communism, and the Fascist and their ideology is now prominent within the Western Empires. Germany is using economic to dominate Western Europe instead of military invasions.
An example of winning the war but losing the peace can be seen in the Vietnam War, the Haitian Revolution, the Black Power Struggle, the African Decolonization Struggle, the US invasions of Afghanistan and Iraq.
I prefer winning the war and sustaining the peace, or not allowing the enemy to co-opt or corrupt the peace.