You can, with moderate determination, take a day trip there. https://www.mywanderlust.pl/daytrip-to-transnistria/
(I really do mean sliver: it's 20 miles wide at its widest point; even The Gambia--a country which exists along the shores of the river of the same name--manages to get wider).
The conflict gained a resurgence of relevance in the past year after the latest Russian invasion of Ukraine, over fears that the Russian military might attempt to launch an invasion axis from Transnistria, or at least seek to establish a continuous corridor from Transnistria to Russia. And even more recently, the Moldovan governmental instability has also fueled fears that Russia might try to use Transnistria as leverage in Moldova.
His last known whereabouts were in Serbia, and Belgrade - Podgorica have about five flights per day both ways.
You still go through customs when flying private.
Are they expecting every Cessna 172 travelling out-of-country to depart from one of their two international airports?
I wouldn't say any of them were a particularly smart choice.
I assume these are the commercial destinations. Is it out of the question that he chartered a flight?