This paper proposes a new approach and new techniques for on-line monitoring of concurrent programs to ensure that some of their safety properties are not violated. The techniques modify erroneous systems which violate a certain safety property, into new systems which satisfy the safety property by adding a new layer that controls the scheduling of steps in the system. We formally characterize the relationship between the erroneous and the new system. Safety monitors for mutual-exclusion, l-exclusion, and the producer consumer tasks are presented. A proof for the mutual-exclusion task is presented to demonstate the applicability of our approach. Our results are also of significance in the context of evolving systems--systems which are repeatedly modified due to changes in the user requirements, user specifications, or implementation. The monitoring technique proposed here ensures that safety requirements are not violated in such evolving systems, in spite of frequent changes.