Obviously, there are different consequences for the varied scenarios or activities laid out above. However, the university is most vulnerable if one of its researchers omits pertinent information about foreign nexuses on a grant application. Not only will the researcher be subject to criminal and civil penalties (see Foreign Influence in the News), but the university itself could be implicated under the False Claims Act (FCA), which governs materially false statements or omissions that could "influence, or be capable of influencing, the payment or receipt of money or property." There are many examples of universities that have had to repay enormous sums of money, i.e., up to three times the amount of the original award ("treble damage") plus additional penalties for each paid false invoice. It is critical that principal investigators and other key or senior research personnel be completely transparent in the university's conflict of interest forms and grant proposal disclosures. If, at any stage of an application, you are unsure whether you have an outside interest that should be disclosed, contact our office or simply err on the side of caution and disclose it.
More information on disclosure requirements can be found here and here.