Current reconfiguration techniques are based on starting the system in a consistent configuration, in which all participating entities are in their initial state. Starting from that state, the system must preserve consistency as long as a predefined churn rate of processors joins and leaves is not violated, and unbounded storage is available. Many working systems cannot control this churn rate and do not have access to unbounded storage. System designers that neglect the outcome of violating the above assumptions may doom the system to exhibit illegal behaviors. We present the first automatically recovering reconfiguration scheme that recovers from transient faults, such as temporal violations of the above assumptions. Our self-stabilizing solutions regain safety automatically by assuming temporal access to reliable failure detectors. Once safety is re-established, the failure detector reliability is no longer needed. Still, liveness is conditioned by the failure detector's unreliable signals. We show that our self-stabilizing reconfiguration techniques can serve as the basis for the implementation of several dynamic services over message passing systems. Examples include self-stabilizing reconfigurable virtual synchrony, which, in turn, can be used for implementing a self-stabilizing reconfigurable state-machine replication and self-stabilizing reconfigurable emulation of shared memory.