Homing and synchronizing sequences (HSs and SSs) are used in Finite State Machine (FSM)-based testing for state identification when deriving a test suite with guaranteed fault coverage or when performing a non-intrusive (passive) testing or monitoring. However, such preset sequences do not always exist for nondeterministic FSMs or can be rather long if existing. Adaptive HSs and SSs are known to exist more often and can be much shorter which makes them attractive for deriving test suites and adaptive checking sequences. As nowadays, a number of specifications are represented by nondeterministic FSMs, there is a need for the deeper study of such sequences, their derivation strategies, and related complexity estimation / reduction. In this paper, given an FSM and a subset S′ of its states, we are concerned with the existence check and derivation of S′-homing and S′-synchronizing adaptive sequences (test cases) which allow to reduce the uncertainty about the current state of the FSM up to a state of the subset S′. There are a number of research papers on evaluating the complexity of the existence check of adaptive HS / SS as well as on estimating the length of an HS / SS, and in the ICTSS’19 conference, we presented the complexity of their derivation for non-initialized complete nondeterministic FSMs. In this paper, we utilize the criteria of the ICTSS’19 paper to estimate the complexity of the existence check and derivation of S′-homing and S′-synchronizing test cases for non-initialized observable nondeterministic FSMs. Some sufficient conditions for weakly initialized FSMs to have adaptive S′-homing and S′-synchronizing test cases are also established.