I checked and FunctionTestCase seems to completely break the loader. The tests for FunctionTestCase in the standard library instantiate the class from inside the method of a TestCase so the loader never see them but even the simple test file I attached completely  breaks:

✗ python3 -m unittest
E
======================================================================
Traceback (most recent call last):
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/runpy.py", line 193, in _run_module_as_main
    return _run_code(code, main_globals, None,
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/runpy.py", line 86, in _run_code
    exec(code, run_globals)
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/__main__.py", line 18, in <module>
    main(module=None)
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/main.py", line 101, in __init__
    self.runTests()
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/main.py", line 271, in runTests
    self.result = testRunner.run(self.test)
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/runner.py", line 183, in run
    result.printErrors()
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/runner.py", line 109, in printErrors
    self.printErrorList('ERROR', self.errors)
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/runner.py", line 115, in printErrorList
    self.stream.writeln("%s: %s" % (flavour,self.getDescription(test)))
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/runner.py", line 47, in getDescription
    return '\n'.join((str(test), doc_first_line))
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/unittest/case.py", line 1472, in __str__
    self._testFunc.__name__)
AttributeError: 'str' object has no attribute '__name__'



I look at plenty of usages of FunctionTestCase on Github and all of them seemed to be false positive, they were copies of the unittest/test/test_functiontestcase.py file

The patch in the attached PR is not correct thought, it only fixes one of the loader and all of them suffer from the same issue.