She apparently returned to Sweden for a time and then came back to Chicago on the T.M.S. Kungsholm sailing from Gothenburg on 3/29/1930 and arriving New York on 4/8/1930.She is listed as single, born Stenkvista and shows her father as Gustav Erikson residing in Snickartorp, Hellberga.
I believe the following is your Elna...
1940 Illinois, Cook County, Wilmette, New Trier Township, ED#16-302, Sheet 66A, No Date: Iver Arnson, head, 33yo, Sweden, Naturalized, 1935 Residence Chicago, Gardner/Landscaper Elna, wife, 34yo, Sweden, Alien, 1935 Residence Chicago, No Occupation Kenneth, son, 3yo, IL
Social Security Death Index: Elna M. Arnson b.8/8/1906 d.2/10/1994, last residence, Rockford, Winnebago Illinois Iver Arnson b.10/13/1906 d.9/19/1996, last residence Rockford, Winnebago Illinois *Both are indexed as having obituaries in the Chicago Tribune...Elna 2/12/1994 and Iver 9/20/1996.
Swedish Birth Records: Elna Maria b.8/8/1906 in Stenkvista, Sodermanland to parents Lars Gustaf Eriksson b.11/23/1869 and Erika Charlotta Sandberg b.3/24/1870.