  Violation of a Bell inequality certifies that the underlying state must be
entangled in a device-independent way, although there may exist some entangled
states which do not violate such an inequality. On the other hand, for every
entangled state, it is possible to find a hermitian operator called
entanglement witness that can detect entanglement through some local
measurements in a device-dependent method. The methods are significantly
fragile to lossy detectors. To avoid such difficulties,
measurement-device-independent entanglement witness based on a semi-quantum
nonlocal game was proposed which turns out to be robust against lossy
detectors. We employ here such a measurement-device-independent entanglement
witness to detect entanglement in a scenario where half of an entangled pair is
possessed by a single observer while the other half is with multiple observers
performing measurements sequentially, independently, and preserving
entanglement as much as possible. Interestingly, we find that the numbers of
successful observers who can detect entanglement measurement
device-independently, both with equal and unequal sharpness quotients, are
higher than that obtained with standard and Bell inequality-based entanglement
detection methods, reflecting its robustness. The entanglement contents of the
sequentially shared states are also analyzed. Unlike other scenarios, our
investigations also reveal that in this measurement-device-independent
situation, states having entanglement in proximity to maximal, remains
entangled until two sequential observers even if they measure sharply.
