This seems like the same problem that lifetimes solve in Rust - tracking when values are no longer used and thus fall "out of scope". Automated tooling should really be doing lifetime analysis of these values, and that seems to me like it would fall well out of scope of what GenAI can be trusted to do.
If this is such a huge problem, are you able to create finalizers that close the resources instead, or better abstractions for managing the LTs of these resources? I don't write Java anymore, but this seems like a problem better solved by other tools.