The east side I think is mainly a residential area and split from the other side of town by rivers. The Ukrainians might be able to hold on for some time, if they choose to continue to fight there.
Everyone keeps saying that Bakhmut itself is of much more symbolic than strategic importance. If that is true, and it is the case that Ukraine is only willing to commit X amount of resources to that fight to inflict massive casualties against the Russians while keeping the rest of their forces elsewhere, while the Russians are willing to spend unlimited resources at Bakhmut, then the only real disaster here is if the Ukrainian forces are unable to retreat once Russia taking the city looks both likely and imminent. Maybe the Russians see something that no one else does, I suppose, but there’s been little in this war so far to suggest they deserve the benefit of the doubt in that regard.