Step 1: Understand the stability of Group 14 tetrahalides.
Group 14 elements form tetrahalides in the \(+4\) oxidation state. However, the stability of the \(+4\) oxidation state decreases down the group because of the inert pair effect.
Step 2: Analyze lead tetrahalides.
Lead commonly shows the \(+2\) oxidation state more stable than the \(+4\) state.
Among lead tetrahalides, \(\mathrm{PbCl_4}\) can exist under controlled conditions, but \(\mathrm{PbI_4}\) is unstable because iodide ion is a strong reducing agent.
Step 3: Explain decomposition of \(\mathrm{PbI_4}\).
\(\mathrm{Pb^{4+}}\) oxidizes \(\mathrm{I^-}\) to iodine and itself gets reduced to \(\mathrm{Pb^{2+}}\).
\[
\mathrm{PbI_4\rightarrow PbI_2+I_2}
\]
Hence, \(\mathrm{PbI_4}\) does not exist as a stable compound.
Step 4: Final conclusion.
Therefore, the tetrahalide that does not exist is
\[
\boxed{\mathrm{PbI_4}}
\]