Terms and definitions for regular language and NFA
Let $L$ be a regular language. There exists a NFA for $L$ in which $\delta(q,\sigma)=\varnothing$ (for every final state $q$ and every symbol $\sigma$) if $\lambda\notin L$.

We can make this into a characterization: iff $\lambda\notin L$ or $L = \{ \lambda\}$.