When the industry does start up again, many say, it will be a time to let go of outdated business practices and develop more creative ways to feed people.

这是自由间接引语结构。间接引语作了主句，引述分句many say以插入语的形式出现。when从句并非修饰many say, 而是修饰 it will be... 。改为普通间接引语则为：

Many (people) say that when the industry does start up again, it will be a time to let go of outdated business practices and develop more creative ways to feed people.

引述分句为主句，间接引语为宾语从句。