It should probably be written in better, more modern languages, but rewriting it would be very expensive.

I've never understood this logic. Mainframes are really fucking expenses. Especially 60 year old ones require special vendor contracts. In most cases, we're taking millions of dollar leases per year, just for the hardware. Then add on top of that rent to house the thing and electricity (small, but still significant compared to modern hardware and/or cloud)

Not to mention the software developers. Most cobol programmers are at least $150K + salaries.

And what are we looking at. An unemployment system? That's not an impossible under taking. In fact, it seems pretty mundane and boring. The business logic is very well defined and this has been done many times before.