How will economy find long-term equilibrium in AD-AS model in case of a negative supply shock? Let's suppose that negative supply shock happened that affected SRAS, but not LRAS. Let's also assume that previously there was long-run equilibrium at point $A$. Due to negative supply shock SRAS decreased, meaning that economy will be either at point $B_1$ (real GDP supplied stayed the same, but price level increased) or at point $B_2$ (price level stayed the same, but real GDP supplied decreased). In both cases they will lead to short-term equilibrium at point $C$

But what will happen next? How will the economy find its long-term equilibrium in this situation? Judguing visually, there are two shortest ways to reach long-term equilibrium after negative supply shock. Either SRAS will increase to its old level or AD will increase so much that long-term equilibrium at point $B_1$ will be reached. But I don't see any reasons why would any of them happen (unless the government intervenes by detaxing/deregulating/subsidizing firms or by spending more). If anything, I would expect AD to decrease due to decreased real wealth (real wealth decreased because both inflation increased and GDP supplied decreased). But such shift wouldn't lead to long-term equilibrium. At the least not without consequent increase of SRAS. But why would such consequent increase happen (assuming no government intervention)?
The only way to shift the SRAS curve without also shifting the LRAS curve is through a temporary change in input prices. By definition temporary changes in input prices are temporary, thus they will return to their previous values. Thus the SRAS will return to its previous long-term value at $SRAS_1$