It is shown that the electromagnetic Green's functions of any linear medium with arbitrary heterogeneity can be obtained from the cross-correlation, or the cross-convolution, of two recordings at different receiver locations in an open system. Existing representations are known for cross-correlations where time-reversal invariance is exploited and hence they are considered in lossless media. We show here that the cross-correlation type representations are exact in a configuration with sources on a closed boundary and the medium has non-zero loss terms only outside this boundary. Furthermore, we show that for cross-convolution representations the loss mechanisms may exist anywhere in space. Many sources of electromagnetic signals exist in the atmosphere and in populated areas, and these can be used in a large variety of practical passive applications exploiting eddy current or electromagnetic wave techniques.