It's claimed that there are zillions of lines of COBOL code (or some large number) out there running most of the infrastructure of modern life, and that as the knowledge of how to maintain these systems disappears from the job market due to technological change and the ravages or mortality, this could result in some great calamity (doom perhaps?). I think this is unlikely. Most businesses - especially large ones - know all about the problems of obsolescence, particularly of software and electronics, and businesses which don't plan for obsolescence are not really viable on any medium to long term time scale.
It may be the case that financial industries are not traditionally accustomed to planning for technological obsolescence. It's worth remembering that the conversion of accounting from paper to electronic formats largely took place only within the previous three or four decades. In a paper based world you don't need to think about these issues, and technology was limited to things such as typewriters which remained quite static over long periods of time. Paper archives also didn't need to be periodically translated into different languages, and methods of processing paper, in terms of filing cabinets and indexes, probably also didn't change much from one decade to the next.
Large amounts of old code can sometimes also be replaced by much smaller amounts of newer code, since as time passes much of the low level details get abstracted away by use of libraries or higher level languages. I actually have a qualification in COBOL programming, and can confirm that it is indeed a diabolical carbuncle, but probably made some sense in the 1960s and 70s. As I remember much of COBOL was heavily oriented around a very particular sort of printer technology, which makes little sense in today's world especially if not much actually gets printed out.

So I don't think it's worth losing any sleep over the collapse of COBOLitarianism, and it's demise should be cause for celebration rather than mourning. Most large business owners don't want to see their enterprises destroyed through negligence, and as the need to replace old back end systems arises they will be replaced, with little or no apparent change as far as the customer is concerned.