Saverin likely renounced his U.S. citizenship in part for tax reasons. However, my impression is he took something of a tax gamble and probably lost. He was expecting to renounce "quietly," or at least hoped so, but that didn't happen. The vast majority of his wealth and income is still U.S. source, so it's rather hard to understand what he was doing or thinking. He also undoubtedly damaged or destroyed his top line potential going forward -- he's rather toxic in business terms.
To my knowledge Saverin has not attempted entry into the U.S. since his renunciation. He would be wise not to test that, and I assume his attorneys have said much the same. If he did manage to enter the U.S. it'd probably be his only and last visit since Congress would likely close the doors tightly. He still has family in the U.S., so when/if one of them is on a death bed he might attempt a visit. He has to choose that test very carefully.
He appears to be "lying low" (in playboy terms anyway), and that's a good idea.
