Corrective control theory ensures the robust operation of asynchronous sequential machines subject to transient faults. This note is concerned with the problem of fault-tolerant corrective control when the reachability of the asynchronous machines fails to satisfy the existence condition for a corrective controller. We show that with limited reachability, the closed-loop system may recover the normal input/state specification within a bounded delay. Delay-bound controllability and the maximum allowable delay for a given asynchronous machine are analyzed in the framework of corrective control. An algorithm for controller design is presented and demonstrated in an example.