By half min decoder, I mean a decoder that is 1) efficient 2) always corrects if there are less than or equal to d/2 errors and 3) always fails if there are more than d/2 errors. Can such hypothetical decoders exist?
Say we have a $q$-ary code of length $n$ and minimum distance $d$. If one uses a traditional half-minimum distance decoder that corrects all errors of upto $\lfloor\frac{d}{2}\rfloor$ precisely, then is the corrected vector $\underline{ALWAYS}$ wrong if the number of errors in the vector before correction is $\lfloor\frac{d}{2}\rfloor + 1$? If not, then for what fraction of error vectors beyond half min distance does the decoder always fail?
There are several misconceptions in your notions about what happens with bounded-distance decoders, and especially in the case when the number of errors is exactly equal to $\frac{d}{2}$ where $d$ is the minimum distance of the code.
Suppose that $\mathbf c$ is the transmitted codeword and $\mathbf r$ is the received word. By definition, a $t$-error-correcting bounded-distance decoder produces the unique codeword $\hat{\mathbf{c}}$ (if such a codeword exists) that is at distance $t$ or less from the received word $\mathbf{r}$. Here, $t \leq \frac{d-1}{2}$ where $d$ is the minimum distance of the code.
If $t$ or fewer errors have occurred, then the codeword $\hat{\mathbf{c}}$ that the decoder produces is $\mathbf c$, and the decoder has operated exactly as we want it to operate: it has determined the transmitted codeword correctly.
If $d-t$ or more errors have occurred, there might be a different (unique) codeword $\hat{\mathbf{c}}$ that is at distance $t$ or less from $\mathbf r$, and in this case, the decoder will produce $\hat{\mathbf{c}}$. This event is called a decoder error. The occurrence of such an event is not something that the decoder can detect, and the wrong codeword is thus sent on to its destination.
It is also possible that there is no codeword at distance $t$ or less from $\mathbf r$, and in this case, the decoder will not produce a codeword at all, but will provide an indication to the effect that there is no codeword at distance $t$ or less from $\mathbf r$.
If $t < \frac{d-1}{2}$, then in the "no-man's-land" where the number of errors is more than $t$ and less than $d-t$, the $t$-error-correcting bounded-distance decoder will always fail and indicate that there is no codeword within distance $t$ of the received word. It might be that the actual number of errors is smaller than $\frac{d-1}{2}$ and so $\mathbf c$ is the unique codeword that is closest to the received word $\mathbf r$. It might even be that the decoder is able to determine that this is the case, but since it is constrained to correct no more than $t$ errors, it nonetheless indicates that $\mathbf r$ cannot be decoded into a codeword at distance $t$ or less from $\mathbf r$.
When $d$ is an even number, and exactly $\frac{d}{2}$ errors have occurred, there might be two codewords that are at distance $\frac{d}{2}$ from the received word: the codeword $\mathbf{c}$ actually transmitted and another codeword $\hat{\mathbf c}$. Thus, a $\frac{d}{2}$-error-correcting bounded distance decoder does not exist in the sense that no decoder can guarantee that all possible patterns of $\frac{d}{2}$ or fewer errors will result in the transmitted codeword being determined correctly. Variations of decoders such as list decoders that produce a list of most likely transmitted codewords can be used in such cases, but these are not called bounded-distance decoders in the sense described above.