A friend's father is a COBOL programmer. He works for a bank (shocker!) and has said that while there are jobs they are not available all over the country but mostly limited to certain areas. So while a Java or PHP programmer will be able to find work pretty much anywhere a COBOL programmer might only find a dozen companies with openings and mostly in places like London, New York, etc. Places with big financial institutions.
I've heard this, but whenever I've looked at job listings for COBOL they pay is much lower than for a similarly skilled Python or Java developer.
I would think COBOL jobs are probably secure, they are not going to get rid of you quickly with few people available to replace you, but they are not abundant.
I think situations like that are a double edged sword. Sure they are in demand but maybe it also requires them to move to another place or even move around a lot which might be incompatible with other lifestyle choices.
Not sure about COBOL but RPG programmers are still highly sought after by large, moated institutions.