I'm pretty sure there's already a system to transpile COBOL to Java without resorting to LLMs.
But I agree, it doesn't make sense to risk bugs just for that.
But their business cases were similar to what we see now with LLMs.
* use some kind of deterministic transpilation that creates ugly code which for sure reproduces the same behaviors
* add tests to cover all those behaviors
* refactor the ugly code
From my experience with copilot I guess that a LLM could help a lot with steps 2 and 3, but I wouldn't trust it at all for step 1