The classic 737 has on some models (depending on the options ordered and the MCP version as well as the flight control computer version) the feature that it will revert from VS into Level Change when the speed drops a certain amount below the MCP selected speed. That can be very annoying indeed if that limit is small and the reversion happens at only 5 to 10 kts below the selected speed.
However, that is not installed on all models, we had a quite mixed fleet over the years with around 15 different models (all 733 except one 735) and behaviour can be different between any of them. Quite interesting to see and try out what they do or dont do (wtf is it doing now?). On some of them you can indeed stall the airplane using VS, on others you can't. Best to be carefull using VS.