You seem to describe an auto-antonym, "a word with a homograph (another word of the same spelling) which is also an antonym."

Fixed can be construed as an auto-antonym since it means both "working properly" and "not working properly—because rigged."

Any auto-antonym can be paired with one of its synonyms to create a pair of different words that are both synonyms and antonyms. For example, the pair fixed/broken. It seems doubtful that there is a special name for such pairs.

Here is the complete passage from Wikipedia which gives many alternative names for the phenomenon:

An auto-antonym (sometimes spelled autantonym), or contronym (also spelled contranym), is a word with a homograph (another word of the same spelling) which is also an antonym (a word with the opposite meaning). An auto-antonym is alternatively called an antagonym, Janus word (after the Roman god), enantiodrome, self-antonym, antilogy, or addad (Arabic, singular didd). It is a word with multiple meanings, one of which is defined as the reverse of one of its other meanings. This phenomenon is called enantiosemy, enantionymy or antilogy.