The “loose-meat sandwich” is usually identified with the Maid-Rite restaurant chain (since 1926) in Iowa. However, a “loose meat sandwich” was advertised for sale in a Harlingen, TX drive-in in 1952, and it’s one of the earliest cites for the sandwich. A “Yum-Yum” sandwich shop (cited below) in Nebraska also served loose-meat sandwiches in the 1950s.
   
Loose-meat sandwiches consist of ground or shredded beef on a bun. Some loose-meat sandwiches resemble sloppy joes.
   
 
Maid-Rite Corporation
Unique Loose Meat Sandwich
In 1926, Fred Angell, a respected butcher in Muscatine, Iowa, combined a special cut and grind of meat with a selected set of spices and created the one and only Maid-Rite sandwich.
As legend goes, Mr. Angell asked a delivery man, at his restaurant, to taste his newest sandwich creation. After a few bites, the taster exclaimed, “You know, Fred, this sandwich is just made right.” Thus our signature sandwiches name was born. Maid-Rite has withstood the test of time for over 80 years.
 
From our humble beginnings of a restaurant owned by a man with a dream of serving great tasting food, the sandwich that was “TOO GOOD TO BE A PATTY” was established. Maid-Rites are cooked in a delicious special seasoning in our special cut of ground beef and served on a warm home-maid bun.
     
Wikipedia: Maid-Rite
Maid-Rite is one of America’s first quick service casual dining franchise restaurants. Before it became a restaurant chain, it was a single restaurant, opened in 1926 by Fred Angell. By the end of the 1920s, there were four franchises granted; these four restaurants are still in operation. Maid-Rite Corporation’s CEO and president is Bradley L. Burt. The corporate headquarters are located in Urbandale, Iowa. As of April 2006, Maid-Rite has over 70 locations, located in Iowa, Nebraska, Illinois, Minnesota, Missouri, and Ohio. The location in Marshalltown, Iowa was featured on the PBS special Sandwiches That You Will Like, and the Quincy, Illinois location was featured in the Food Network Show Feasting on Asphalt. The restaurant chain is not the unnamed restaurant mentioned in Roseanne, which served as the inspiration for the loose meat sandwiches served at the Lanford Lunchbox.
 
History
Angell was a butcher in Muscatine, Iowa, who combined a special cut and grind of meat with a selected set of spices and created the Maid-Rite sandwich, which is not a traditional hamburger. Rather, it is called a “loose meat” sandwich. While the component meat is similar, the Maid-Rite sandwich’s meat is not formed into a patty, making it similar to a sloppy joe only without the tomato-based sauce. After a customer sampled the food, the customer exclaimed that the sandwich was “made right.” Angell modified the “made” to “maid,” reflecting the wholesomeness of the sandwich.

(Dictionary of American Regional English)
loose-meat sandwich  n esp IA Cf. sloppy joe.
A sandwich of ground or shredded beef served on a bun.
1986 DARE File seSD, Reported orally from a Milwaukee, Wisconsin resident: “In Yankton, SD, a sloppy Joe is called a loose-meat sandwich.”
 
27 July 1951, Le Mars (Iowa) Semi Weekly Sentinel, pg. 1, col. 3:
When asked about student preferences, Miss Watson replied “I think they prefer loose meat sandwiches, such as taverns.”
   
12 March 1952, Valley Morning Star (Harlingen, TX), pg. 10, col. 2 ad:
Scotty’s Loose Meat Sandwich
(The Chick Inn—ed.)
 
15 July 1957, Harlan (Iowa) News Advertiser, pg.1, col. 4:
The menu calls for loose meat sandwiches, hot dogs, potato chips, soft drinks, ice cream and milk, Wigness said.
 
17 November 1960, Lincoln (NE) Evening Journal, pg. 16, col. 2:
Lots of readers have expressed interest in Yum-Yums. Yum-Yum is a trademark registered in the state of Nebraska and other states and the recipe is copyrighted and cannot be disclosed. A recipe carried earlier in this column from a reader for a loose meat sandwich is not the Yum-Yum recipe used by franchise owners, Margaret Holman and Genevieve Kundert, and the Yum-Yum Sandwich Hut in Lincoln.
   
22 November 1960, Lincoln (NE) Evening Journal, pg. 7, col. 1:
Several requests for recipes today. One from Mrs. Edwin Knapp of Cortland, who would like a recipe for a loose meat sandwich that does not call for tomato sauce and is not like a barbecue recipe.
 
Google Books
How We Talk:
American Regional English Today
Boston, MA: Houghton Mifflin
2000
by Allan A. Metcalf
Pg. 116:
The loose-meat sandwich is indeed made of loose meat: ground or shredded beef on a bun. It is a specialty of Iowa’s Maid-Rite restaurants, where the loose meat is always steamed, not fried. When you buy a Maid-Rite sandwich, you get a spoon to scoop up the meat that falls out of the bun. Taylor’s Maid-Rite in Marshalltown, Iowa, will ship frozen loose-meat sandwiches anywhere in the country, with pickles and onions on the side. 
   
Google Books
Sex-Crime Panic:
A Journey to the Paranoid Heart of the 1950s
by Neil Miller
Los Angeles, CA: Alyson Publishing
2002
Pg. 49:
In one of the trial’s lighter moments, Tacy questioned the police lieutenant about an interest his wife had in a Sioux City establishment, Ye Old Tavern. “Does your wife have a license to sell beer?” Tacy demanded.
 
“We sell root beer,” aid Dennison.
 
“But it is called a tavern, isn’t it?” Tacy persisted.
 
“That’s because we sell tavern sandwiches,” replied the policeman. (A “tavern sandwich” is Iowa lingo for a loose-meat sandwich, a sloppy joe.)
 
(Trademark)
Word Mark MAID-RITE
Goods and Services IC 029. US 046. G & S: SANDWICHES. FIRST USE: 19250801. FIRST USE IN COMMERCE: 19250801
Mark Drawing Code (1) TYPED DRAWING
Serial Number 72265427
Filing Date February 24, 1967
Current Filing Basis 1A
Original Filing Basis 1A
Published for Opposition July 9, 1968
Registration Number 0857586
Registration Date September 24, 1968
Owner (REGISTRANT) MAID-RITE PRODUCTS, INC. CORPORATION IOWA 110 CEDAR ST. MUSCATINE IOWA 52761
Assignment Recorded ASSIGNMENT RECORDED
Attorney of Record A. YATES DOWELL, III
Prior Registrations 0226237;0545064;AND OTHERS
Type of Mark TRADEMARK
Register PRINCIPAL
Affidavit Text SECT 15.
Renewal 1ST RENEWAL 19880924
Live/Dead Indicator LIVE