1. We need to identify which compound does not exist among the given options.

2. Check each option:

Option A: $(\mathrm{NH_4})_2\mathrm{BeF_4}$

This is ammonium tetrafluoroberyllate.

• Beryllium forms the complex ion $[\mathrm{BeF_4}]^{2-}$.
• With two $\mathrm{NH_4^+}$ ions, the salt $(\mathrm{NH_4})_2\mathrm{BeF_4}$ is feasible.

So, this compound exists.

Option B: $\mathrm{PbEt_4}$

Here $\mathrm{Et}$ means ethyl group $(-\mathrm{C_2H_5})$.

• $\mathrm{PbEt_4}$ is tetraethyl lead.
• This is a well-known organolead compound.

So, this compound exists.

Option C: $\mathrm{BeH_2}$

• Beryllium hydride is a known compound.
• It exists as a polymeric covalent solid rather than as simple discrete molecules under normal conditions.

So, this compound exists.

Option D: $\mathrm{NaO_2}$

This would imply sodium superoxide.

• Alkali metals form different oxygen compounds depending on cation size:
  • $\mathrm{Li}$ forms oxide: $\mathrm{Li_2O}$
  • $\mathrm{Na}$ mainly forms peroxide: $\mathrm{Na_2O_2}$
  • larger cations like $\mathrm{K, Rb, Cs}$ form superoxides: $\mathrm{KO_2, RbO_2, CsO_2}$
• Sodium superoxide $\mathrm{NaO_2}$ is generally not considered a stable/existing normal compound in this context.

So, this compound does not exist.

3. Therefore, the correct option is:

$\boxed{\mathrm{NaO_2}}$

So the answer is Option D.