What would happen to the idea of peaceful co-existence as a result of this crisis?

The correct answer to this open question is the following.

Unfortunately, you did not mention what crisis you are referring to.

Without that information, we do not know what you are talking about.

However, trying to help, we can assume you are talking about the Cold War crisis because it was the Soviet Union that coined that phrase after the Cold War years.

So if that is teh case, what would happen to the idea of peaceful co-existence as a result of this crisis was that the two world superpowers of that time -the Soviet Union and the United States- had to learn to live in relative coexistence and "peace," after so many years of competing in the arms race, the space race, and the spread-containment of Communism around the world.

These countries had to learn how to coexists, more for necessity, rather than conviction.

basic principles: federalism, separation of powers, checks and balances, judicial review, representative democracy, limited government, rule of law, individual rights and responsibilities, consent of the governed, majority rule, popular sovereignty, equal protection.