Earlier quoted context omitted.
COBOL is unstructured. It doesn't even have functions. When you've got some million+ line tangled mass that has all kinds of undocumented behavior, it's really better just to add more duct tape and punt it off to the poor bastard who actually has to fix it in 20 years.
Since 1985 that COBOL can be structured, and since 2002 object oriented as well, with the latest ISO update being done in 2014 Besides compiling to native code, there are compilers that target JVM and CLR as well.
So could you wrap it and slowly add new features and replace pieces with Java code over time, using JVM for interop?