With over-the-air latency on the order of 0.1ms an-ticipated in 6G systems, the practical design of Finite-Blocklength Coding (FBC) has the potential to achieve extremely low latency communications. For this purpose, we focus on a joint FBC scheme in multi-user downlink systems. With a requirement of extremely low latency, we jointly encode data bits of multiple users over their orthogonal channel resources. As a result, we obtain throughput gain of the downlink transmission by an enlarged blocklength of FBC. In particular, we first present the joint encoding design for multiple downlink users by a matrix-based method. Under the multi-user joint FBC scheme, we then formulate an Integer Programming (IP) problem to maximize the throughput of downlink users subject to an average constraint on transmission power. By converting the derived IP problem to a nonlinear bipartite matching problem, we finally present a unified algorithm to obtain the optimal power-constrained throughput within the low latency requirement.