Can two nonzero signals $x[n]$ and $y[n]$ give a zero convolution
Yes, for example let

$$x[k]=1$$

for all $k$ and

$$y[k] = \begin{cases}1 &amp; k=0\\-1 &amp; k=1\\0 &amp; otherwise \end{cases}$$

It is easy to see that in case of a convolution, the result will be zero for all values of $n$.