There seems to be two Scheid-Kloss marriages. I see an Agatha Kloss who had a son Michael Scheidt in 1898 (husband by same name), but that is after the dod you have. In the 1860 census I see this possibility for your Eliz:
1860 United States Federal Census
Name: Elizth Klaus
Birth Year: abt 1853
Birthplace: Illinois
Home in 1860: Township 2 Range 7, St Clair, Illinois
Gender: Female
Post Office: O Fallon
Household Members:
Peter Klaus 42, b. Prussia; farmer
Elizth Klaus 35, b. Bavaria
Cathrine Klaus 16 [all children b. Ill.]
Peter Klaus 13
Margaret Klaus 9 [Agatha?]
Elizth Klaus 7
Henry Klaus 5
Louisa Klaus 2
The 1880 census says Eliz's father was b. Prussia (may appear as Germany):
1880 United States Federal Census
Name: Elisabeth Scheidt
Home in 1880: Bloom, Cook, Illinois
Estimated birth year: abt 1851
Birthplace: Illinois
Relation to Head of Household: Wife
Spouse's name: Michael
Father's birthplace: Prussia
Mother's birthplace: Prussia
Occupation: Keeping House
Marital Status: Married
Race: White
Gender: Female
Household Members:
Michael Scheidt 31
Elisabeth Scheidt 29
Michael Scheidt 6
Salomie Scheidt 2
John Scheidt 3M
Looking in Bloom Twp in 1870 there are these two families which Eliz could have belonged to:
1870 United States Federal Census
Name: John Klass
Birth Year: abt 1804
Birthplace: Prussia
Home in 1870: Bloom, Cook, Illinois
Race: White
Gender: Male
Post Office: Dyer
Household Members:
John Klass 66
Catharine Klass 59
Louisa Klass 18
John Klass 20
Peter Klass 19
1870 United States Federal Census
Name: John Klass
Birth Year: abt 1827
Birthplace: Deutschland
Home in 1870: Bloom, Cook, Illinois
Race: White
Gender: Male
Post Office: Dyer
Household Members:
John Klass 43
Anes Klass 41
Louisa Klass 19
Juliaann Klass 17
Barbara Klass 15
Josephine Klass 13
John Klass 11
Celestina Klass 9
Rosena Klass 5
Agnes Klass 2
According to the 1900 census, Agatha Kloss Scheid was b. Sep 1868, and her husband, MS, in Aug 1858, so likely a different MS:
1900 United States Federal Census
Name: Agnes Scheidt
Home in 1900: Bloom, Cook, Illinois
Birth Date: Sep 1868
Birthplace: Illinois
Race: White
Gender: Female
Relationship to Head of House: Wife
Father's Birthplace: Germany
Mother's Birthplace: Germany
Mother: number of living children: 4
Mother: How many children: 4
Spouse's name: Michael
Marriage Year: 1895
Marital Status: Married
Years Married: 5
Occupation:
Household Members:
Michael Scheidh 41, b. Aug 1858 [so a different MS]
Agnes Scheidt 31
Agnes Scheidt 10
Theressa Scheidt 6
Julia Scheidt 3
Michael B Scheidt 1 [the child whose birth I saw]
George Schmidt 30
Here's a website with something on Eliz's daughter Salomie Hilbrich:
http://waynekuntze.com/wk12dec08/pafn56.htmDeath certificate of 29 Dec 1945 in file. Died of acute myocarditis (3 weeks) and carsonoma of liver (6 months). Parents given as Michael SCHEIDT, Alsace-Lorraine Germany and Elizabeth KLOSS, Strasburg [Shelby Co], Illinois. Age was 67 years, 10 months, and 14 days. Informant was Edward P. HILBRICK of 915 W 53rd Street, Chicago, Illinois. Birth date was 15 Feb 1878. Lived 15 years at death location, 915 W 53rd Street.
See also
http://www.waynekuntze.com/wk12dec08/pafg56.htm So, nothing conclusive, but maybe some ideas for your search.