The ambiguity starts from the C Standard itself. Both C99 and C11 have identical description of snprintf function. Here is the description from C99:
7.19.6.5 The snprintf function
Synopsis
1 #include <stdio.h>
int snprintf(char * restrict s, size_t n, const char * restrict format, ...);
Description
2 The snprintf function is equivalent to fprintf, except that the output is written into an array (specified by argument s) rather than to a stream. If n is zero, nothing is written, and s may be a null pointer. Otherwise, output characters beyond the n-1st are
discarded rather than being written to the array, and a null character is written at the end of the characters actually written into the array. If copying takes place between objects that overlap, the behavior is undefined.
Returns
3 The snprintf function returns the number of characters that would have been written had n been sufficiently large, not counting the terminating null character, or a negative value if an encoding error occurred. Thus, the null-terminated output has been completely written if and only if the returned value is nonnegative and less than n.
On the one hand the sentence
Otherwise, output characters beyond the n-1st are discarded rather than being written to the array, and a null character is written at the end of the characters actually written into the array
says that
if (the s points to a 3-character-long array, and) n is 3, then 2 characters will be written, and the characters beyond the 2nd one are discarded; then the null character is written after those 2 (and the null character will be the 3rd character written).
And this I believe answers the original question.
THE ANSWER:
If copying takes place between objects that overlap, the behavior is undefined.
If n is 0 then nothing is written to the output
otherwise, if no encoding errors encountered, the output is ALWAYS null-terminated (regardless of whether the output fits in the output array or not; if not then some characters are discarded such that the output array is never overflown),
otherwise (if encoding errors are encountered) the output can stay non-null-terminated.
On the other hand
The last sentence
Thus, the null-terminated output has been completely written if and only if the returned value is nonnegative and less than n
gives ambiguity (or my English is not good enough). I can interpret this sentence in at least two ways:
1. The output is null-terminated if and only if the returned value is nonnegative and less than n (which means that if the returned value is not less than n, i.e. the output (including the terminating null character) does not fit in the array, then the output is not null-terminated).
2. The output is complete (no characters have been discarded) if and only if the returned value is nonnegative and less than n.
I believe that the interpretation 1 above contradicts THE ANSWER, causes misunderstanding and lengthy discussions. That is why the last sentence describing the snprintf function needs a change in order to remove any ambiguity (which gives grounds for writing a Proposal to the C language Standard).
The example of non-ambiguous wording I believe can be taken from http://en.cppreference.com/w/c/io/fprintf (see 4)), thanks to @"Martin Ba" for the link.
See also the question "snprintf: Are there any C Standard Proposals/plans to change the description of this func?".