Short to mid-term, the administration will keep the worst at bay with their reserves, that is, throw just enough heat into the system to stop pipes from freezing, while people will move over the border (it's not like it's a frontline or they're not Moldovans) while the administration figures out a deal with Chisinau. It's like that they can't gas from the rest of Moldova which can get it from Romania which can get it from the wider European network, it's just that they're not used to paying for it. Chisinau itself has an interest in supplying Transnistria because the Moldovan electricity grid is fickle at best without the Transnistrian plant and the connections to Romania aren't beefy enough to stabilise it. That's a temporary limitation, though, it's a weakness in negotiation position that Chisinau can fix quite easily.

Longer term though Transnistria's economical situation is fucked because they're used to that free energy and I doubt they can increase productivity etc. to still be competitive now that that's gone. No industry, no workers (they'll move across the border at least to work), no funds for pension payments. Thinkable is a generous amnesty for shady businesspeople (i.e. the government) in exchange for not making a stink about reintegration, probably with plenty autonomy and cleaning up the corruption with, in one way or the other, European oversight... for maybe a different reason than you think: Chisinau isn't exactly stellar about minority politics, ask the Gagauzians, it's mostly benign neglect, general disinterest. EU diplomats have been all over the place mediating and making sure that Chisinau actually gives a fuck, made sure EU funds also find their way into non-Romanian speaking areas, they're bound to do the same with Transnistria.

In maybe too few words: The EU is going to put money on the table and buy the place before it Balkanises, good ole chequebook diplomacy. Hard to hate your neighbours when their friends are having the lot of you over for dinner.