Your point is well taken. Immigration may well make things worse, or just be an exchange one set of survival challenges for another. I suppose the other main option is toughing it out and trying to be one of those who help to rebuild and restore, which ties into Tom L's insightful comment about long-term survival being a community thing.

As to emigration, I note that many Jews and others who wisely fled antebellum Nazi Germany for other European nations soon found themselves victims of the Nazis nonetheless, as Germany overran those countries in WWII. Interestingly, some ex-Confederates after the Civil War and ex-Nazis after WWII were able to persevere in what might be termed survival enclaves in South America, and surviving European Jewish emigres helped found the modern state Of Israel. Today, some Central American nations host large emigre communities of ex-pat Americans and others. It pays to choose your destination early, but carefully.

In a global catastrophe, I suppose those already dedicated to pursuing a maximally self-sufficient and off-grid lifestyle may find themselves in a final battle for survival with those who were able to use extreme wealth and/or power to insulate themselves from the consequences of total collapse until near the end. The world of science fiction often explores these possibilities and provides many interesting takes on both the causes of, and the means of survival in, a global catastrophe.