Then if your query is "what documents contain 'generic'?", you look in the index for "gener" and then open each of those documents and check if it actually has "generic" using a stricter stemmer (that accepts generic{,s}, genericness{,es}, genericit{y,ies}, generically ... this is a bit of a bad example since they all have the prefix directly). The cost is acceptable as long as both words have about the same frequency so it doesn't affect the big O.
Of course if you have any decent kind of compute, you can hard-code exceptions before building the index (which does mean you have to rebuild the index if your exception list changes ... or at least, the part of the index for the specific part of the trie whose exception lists changed - you don't do a global lookup!) to do less work at query time. But regardless, you still have to do some of this at query time to handle nasty cases like lie/lay/laid (searching for "lie" should not return "laid" or vice versa, but "lay" should match both of the others) or do/does/doe (a more obviously unrelated example).