At the start of the year, the Russian economy looked to be giving way. Under the strain of war and sanctions, revenues were falling, production was shrinking and trade was running low. With rising tariffs, credit was prohibitively expensive and borrowing all but impossible: A wave of bankruptcies was on the horizon. In late January, Russia was forced to sell oil to India at just $22 per barrel, about a third of the market rate. As a symbol of unsustainability, it was hard to beat. President Vladimir Putin has heard such complaints throughout the war. Yet, according to those around him, he has chosen largely not to listen. Officials and business leaders, for their part, understood that the continuation of the war was his absolute priority and that the country's economic situation was of little consequence. But in February something shifted. Mr. Putin began, suddenly, to pay attention to the flagging economy. There were even signs he might be changing his mind on negotiations with Ukraine, perhaps seeking an exit from the conflict.