Step 1: The key phrase is detecting cases that the routine system has missed. Match this to the correct type of surveillance.
Step 2: Sentinel surveillance works through a few high-quality reporting points that act as sensors for the whole population. Its defining purpose is to uncover under-reported or missing cases and to supplement officially notified figures, which is exactly what the question describes. India applies it within the National AIDS Control Programme.
Step 3: Compare the alternatives. Passive surveillance simply receives data that flow in on their own as patients seek care, so missing cases stay missing. Active surveillance involves the system going out to gather data, such as fortnightly malaria blood slides, but it is not framed around recovering missed cases.
Step 4: A prevalence rate is merely a frequency measure and detects nothing. So the method designed to catch missing cases is sentinel surveillance.
\[\boxed{\text{Sentinel surveillance}}\]