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We study a well-known communication abstraction called Byzantine Reliable Broadcast (BRB). This abstraction is central in the design and implementation of fault-tolerant distributed systems, as many fault-tolerant distributed applications require communication with provable guarantees on message deliveries. Our study focuses on fault-tolerant implementations for message-passing systems that are prone to process-failures, such as crashes and malicious behavior. At PODC 1983, Bracha and Toueg, in short, BT, solved the BRB problem. BT has optimal resilience since it can deal with t < n/3 Byzantine processes, where n is the number of processes. The present work aims at the design of an even more robust solution than BT by expanding its fault-model with self-stabilization, a vigorous notion of fault-tolerance. In addition to tolerating Byzantine and communication failures, self-stabilizing systems can recover after the occurrence of arbitrary transient-faults. These faults represent any violation of the assumptions according to which the system was designed to operate (provided that the algorithm code remains intact). We propose, to the best of our knowledge, the first self-stabilizing Byzantine fault-tolerant (BFT) solution for repeated BRB in signature-free message-passing systems (that follows BT's problem specifications). Our contribution includes a self-stabilizing variation on a BT that solves a single-instance BRB for asynchronous systems. We also consider the problem of recycling instances of single-instance BRB. Our self-stabilizing BFT recycling for time-free systems facilitates the concurrent handling of a predefined number of BRB invocations and, by this way, can serve as the basis for self-stabilizing BFT consensus.