Putin has turned the exits of major Western companies into a windfall for Russia’s loyal elite and the state itself. He has forced companies wishing to sell to do so at fire-sale prices. He has limited sales to buyers anointed by Moscow. Sometimes he has seized firms outright.Putin has turned an expected misfortune into an enrichment scheme. Western companies that have announced departures have declared more than $103 billion in losses since the start of the war, according to a Times analysis of financial reports. Mr. Putin has squeezed companies for as much of that wealth as possible by dictating the terms of their departure.