Consumers wouldn’t, because they still need things like food and shelter, which they already spend most of their income on. But corporations and wealthy individuals absolutely would. In a deflationary environment, the value of money sitting still in a big savings account goes up while the value of goods and assets goes down. They shift their wealth into whatever vehicle they feel will provide reliable growth.
This was one of the problems we had during the Great Depression. Nobody was investing in new or expanding businesses, so no new jobs were being created.