Let $A \subseteq B$, and A is unrecognizable. I know in general that doesn't mean B is unrecognizable. However, are there some limitations we could put on A and B that would make it true? The only thing I could come up with was A=B. Plus, we could say B is unrecognizable as part of our assumptions, but that's not really helpful.
(recognizable means recursively enumerable, in case you use different terminology)