Moldova's President says on Twitter their border is open and there's a large number of Ukranians arriving, among other places, Palanca, which is I think (?) in the convenient direction, on the Black Sea. I know nothing about the Transnistria situation but there is no Transnistrian territory between Palanca and Ukraine, according to the map on Wikipedia.
- "First citizens arrive in , with over 4000 crossings today. The govt has deployed temporary placement centers near Palanca and Ocnița. Our borders are open for citizens who need safe transit or stay."
https://twitter.com/sandumaiamd/status/1496859315122147337
https://en.wikipedia.org/wiki/Palanca,_%C8%98tefan_Vod%C4%83
edit: also the Prime Minister's photos clearly show that crossing point is open:
- "In these dark days for #Ukraine, we stand by its citizens. Visited the southern crossing of Palanca yesterday. #Moldova will assist those in need of safe transit or shelter. Вітаємо українців!"
https://twitter.com/natgavrilita/status/1497467502904893447