  We demonstrate that linear combinations of subregion entropies with canceling
boundary terms, commonly used to calculate the topological entanglement
entropy, may suffer from spurious nontopological contributions even in models
with zero correlation length. These spurious contributions are due to a
specific kind of long-range string order, and persist throughout certain
subsystem symmetry-protected phases. We introduce an entropic quantity that
measures the presence of such order, and hence should serve as an order
parameter for the aforementioned phases.
