The following is the start of basic corollary in my logic text:
For any set $\Gamma$ of sentences, $\Gamma\subseteq\text{Th}(\text{Mod}(\Gamma))$.
What happens when $\text{Mod}(\Gamma)$ is empty? Suppose $\Gamma={p_1,\neg p_1}$, so that there is no truth value $V$ which models $\Gamma$, or otherwise $V(p_1)=\text{T}=V(\neg{p_1})$, which doesn't respect logical connectives. Then I would have something like $\Gamma\subseteq\text{Th}(\emptyset)$. If I'm working under the definition that $\text{Th}(\emptyset)$ is the set of all tautologies, then this doesn't make any sense.
Should there be an extra condition that $\text{Mod}(\Gamma)$ be nonempty, or am I missing something?