Leftovers were a regular part of food preparation and consumption long before microwaves. Many cultures have traditional recipes that were devised specifically to use up leftovers: In Mexican cuisine, chilaquiles; in British cuisine, bubble and squeak; in Chinese cuisine, fried rice; and in America, turkey à la king and chicken noodle soup.

Salting food was not done for leftovers, that was done to preserve food for a longer period of time---like over an entire winter. Traditionally it was done to large hunks of meat, or a big pile of vegetables at harvest time.

I have a collection of receipt-books (cookbooks) from the 18th and 19th centuries and they are full of recipes which use leftovers. Depending on the household, leftovers might be wrapped in wax paper, or placed in a covered dish and put in a cold storage area like a cellar. They would be used within the next few days.