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I've estimated a model for an fMRI dataset, so I now have a beta_*.nii file for each regressor in my model. In a seperate step, I've defined ROIs using marsbar and proceeded to extract the corresponding voxels in one of these β-maps.

However, the ROI extracted from said β-map contains only NaN values. Why should there be NaNs at all? What does such a null value represent in the context of model βs?

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Apparently, this can happen when your ROI is near the edge of the brain as reported here. The thread is pretty old though so this might have been fixed by today and there is another reason in your case.

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