In this work, we focus on a low-latency multiuser broadcast network operating in the finite blocklength regime and employing a non-orthogonal multiple-access (NOMA) scheme. By letting the user with the stronger channel from the source act as a relay, we propose two relay-assisted transmission schemes, namely relaying and NOMA-relay. We study the finite blocklength performance of the proposed schemes in comparison with the NOMA scheme. Both the average performance of and fairness between users are considered. Our results show that the NOMA scheme is not preferred in the low-latency scenario in comparison to the proposed schemes. In particular, the relaying scheme generally provides the best fairness between users, while the NOMA-relay scheme is able to achieve a higher average throughput by setting the packet size relatively aggressively.