.38-44 ammo was loaded into the 1950s, possibly the early 1960s. Last manufacturer I know of was Remington.
The .357 Magnum didn't instantly displace the .38-44 HD. 6,000 or so .357s were made prior to WW II ending production, most of them the registered magnum. They were VERY expensive for the time, and only individual officers here and there purchased them. Sportsmen purchased the lion's share by far.
No police force adopted the .357 wholesale until at least the 1960s, after introduction of the Combat Magnum (Model 19) and the Highway Patrolman (Model 28), and most police forces, major forces, NEVER adopted the .357 Magnum; they stuck with .38s and went with the +P once that designation came into existence as a standard around 1970.
Things like the Super Vel and other high performance loads available from specialty manufacturers bridged the gap between .38-44 end of production and the origin of the first factory +P loads.
The theory that the .38-44 died out because people were afraid someone would drop one into a Chief's Special doesn't hold water given that no one was particularly worried about the roughly 100,000 or so non-heat treated .38 K frames that were floating around in 1929-1930 when the .38-44 was introduced.
The boxes were clearly marked - don't use these in your K frame or similarly sized guns.
It's very likely that the heat treated cylinder on the Chief's Special would have handled the .38-44 a lot better than would have a circa 1910 K frame.
