Amplitude Modulation with large carrier and suppressed carrier
In short: you can use envelope detection on a suppressed-carrier signal, but you'll recover $|m(t)|$, not $m(t)$.

One easy way to see it is by drawing the signals. Draw an arbitrary signal $m(t)$, which takes positive and negative values. Now draw the signal $s(t)=\cos(2\pi f_ct)\cdot m(t)$. To do this, draw $-m(t)$ on top of $m(t)$, and draw a cosine wave that is "enveloped" by $m(t)$ and $-m(t)$.

To find the envelope of $s(t)$, take its positive part only and draw lines connecting the peaks of the carrier. You'll see that what you obtain is $|m(t)|$.

By the way, the same is true for large carrier modulation; it just turns out that $1+m(t)$ is always positive, so $|1+m(t)|=1+m(t)$.