Statement - I : Potential energy of a system of point charges may be zero.
Statement - II : Potential energy of individual point charges in a system of point charges may be zero.

Potential of system of charges will be $\mathrm{U}=\left[\frac{1}{4{\mathrm{\pi \epsilon }}_0}\sum _{\mathrm{i}=1}^{\mathrm{n}}\sum _{\mathrm{j}=1,\mathrm{i}\equiv }^{\mathrm{n}}\frac{{\mathrm{q}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{j}}}{{\mathrm{r}}_{\mathrm{ij}}}\right]$

So if the summation of $\sum _{\mathrm{i}=1}^{\mathrm{n}}\sum _{\mathrm{j}=1,\mathrm{i}\equiv }^{\mathrm{n}}\frac{{\mathrm{q}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{j}}}{{\mathrm{r}}_{\mathrm{ij}}}=0$, the potential energy of the system will be zero.

Potential energy of individual point charges in a system of point charges may be zero.