This may be a case in which the most common American English style and the most common British English style diverge. In U.S. style, it is quite common to place the end punctuation (the period) within both sets of close quotation marks:
"The victims are showing what the doctors described as 'adverse symptoms.'"
This comports with the general punctuation style recommendations in The Chicago Manual of Style, fifteenth edition (2003), although Chicago does a very poor job of illustrating how to handle a simple .'" situation, preferring instead (at 11.33 Quotations and "quotes within quotes") to use for illustration an example that involves three levels of quotation marks—but an exclamation point as end punctuation. As the authors of Chicago are perfectly well aware, exclamation points and question marks do not follow the same style rules as periods when used as end punctuation in connection with quotation marks in a situation where a sentence ends with a close quotation mark.
Meanwhile, the more common style in UK English, I believe, is to complete the phrase punctuation (the first close quotation mark) before introducing the end punctuation (the period) and the second close quotation mark for the whole-sentence quotation. The only difference in common UK style from the way you illustrate this approach in example (b) of your question is that in UK style the primary level of quotation normally takes single quotation marks and the secondary (internal) level of quotation normally takes double quotation marks. Thus:
'The victims are showing what the doctors described as "adverse symptoms".'
To me, the predominant UK style is significantly more sensible than the predominant U.S. style because it treats the idea within the internal quotation marks as a logical entity to be identified (with the quotation marks) before the writer moves on to closing the sentence as a whole. Any move in the predominant U.S. style toward the main UK style on this point, however, is likely to be slow in coming, owing to the powerful inertial resistance of the established style preference.