The case that solvers report some equivalent to unbounded when they really mean “I found an unbounded ray but not necessarily a feasible point” is precisely why JuMP has the status DUAL_INFEASIBLE instead of UNBOUNDED.
The doc strings are here: MathOptInterface.jl/src/attributes.jl at 8f2f2539e00fd5039f1eccc015b48c69cc925613 · jump-dev/MathOptInterface.jl · GitHub
Feel free to open a PR with suggested improvements. I’ve opened on here: [docs] improve the docstrings of the various enum values by odow · Pull Request #2698 · jump-dev/MathOptInterface.jl · GitHub