  We consider block codes for degraded wiretap channels in which the legitimate
receiver decodes the message with an asymptotic error probability no larger
than $\varepsilon$ but the leakage to the eavesdropper vanishes. For discrete
memoryless and Gaussian wiretap channels, we show that the maximum rate of
transmission does not depend on $\varepsilon\in [0,1)$, i.e., such channels
possess the partial strong converse property. Furthermore, we derive sufficient
conditions for the partial strong converse property to hold for memoryless but
non-stationary symmetric and degraded wiretap channels. Our proof techniques
leverage the information spectrum method, which allows us to establish a
necessary and sufficient condition for the partial strong converse to hold for
general wiretap channels without any information stability assumptions.
