I tried to duplicate your findings in the Philadelphia Directory. I couldn't come up with Katherine Shirley, widow of Richard, 1897. Of course I didn't put a lot of effort into it and my eyes are not what they use to be. In any case:
Catherine Shirley
Date: Tuesday, May 25, 1920 Paper: Philadelphia Inquirer (Philadelphia, PA) Volume: 182 Issue: 146 Page: 21
--------------------------------------------------
FindAGrave.com
Burial:
Leverington Cemetery
Roxborough
Philadelphia County
Pennsylvania, USA
Plot: Lot 23 Section 1 Division D
Donna Elliott
--------------------------------------------------
Name: Richard Shirley
Age: 32
Birth Year: abt 1848
Birthplace: Pennsylvania
Home in 1880: Reading, Berks, Pennsylvania
Race: White
Gender: Male
Relation to Head of House: Self (Head)
Marital Status: Married
Spouse's Name: Kate Shirley
Father's Birthplace: Pennsylvania
Mother's Birthplace: Pennsylvania
Neighbors: View others on page
Occupation: Laborer
Household Members:
Name Age
Richard Shirley 32
Kate Shirley 31
George Shirley 10
Kate Shirley 9
Franklin Shirley 7
Stanten Shirley 6
Louisa Shirley 4
Hannah Shirley 1
Source Citation: Year: 1880; Census Place: Reading, Berks, Pennsylvania; Roll: 1101; Family History Film: 1255101; Page: 68B; Enumeration District: 042; Image: 0302.
--------------------------------------------------
Name: Richard Shirley
Residence Year: 1890
Street Address: 158 Fountain Roxb
Residence Place: Philadelphia, Pennsylvania
Occupation: Peddler
Publication Title: Philadelphia, Pennsylvania, City Directory, 1890
--------------------------------------------------
Name: Richard Shirley
Age: 52
Birth Date: Jul 1847
Birthplace: Pennsylvania
Home in 1900: Exeter, Berks, Pennsylvania
Race: White
Gender: Male
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Amelia Shirley
Marriage Year: 1892
Years Married: 8
Father's Birthplace: Pennsylvania
Mother's Birthplace: Pennsylvania
Occupation: View on Image
Neighbors: View others on page
Household Members:
Name Age
Richard Shirley 52
Amelia Shirley 32
Source Citation: Year: 1900; Census Place: Exeter, Berks, Pennsylvania; Roll: 1376; Page: 7B; Enumeration District: 0018; FHL microfilm: 1241376.
--------------------------------------------------
Name: Geo W Shirley
[Geo W Sherley]
[Geo W Starley]
Age: 50
Birth Year: abt 1870
Birthplace: Pennsylvania
Home in 1920: Philadelphia Ward 21, Philadelphia, Pennsylvania
Race: White
Gender: Male
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Sussie Shirley
Father's Birthplace: Pennsylvania
Mother's Name: Kate Shirley
Mother's Birthplace: Pennsylvania
Home owned: Own
Able to read: Yes
Able to Write: Yes
Neighbors: View others on page
Household Members:
Name Age
Geo W Shirley 50
Sussie Shirley 33
Charles Shirley 25
Rachael Shirley 20
Beatrice Shirley 13
Earl Shirley 8
Roy Shirley 6
Kate Shirley 73
Source Citation: Year: 1920; Census Place: Philadelphia Ward 21, Philadelphia, Pennsylvania; Roll: T625_1617; Page: 1A; Enumeration District: 505; Image: 707.
--------------------------------------------------
I'm going to go out on a limb and say that Richard Shirley probably divorced Catherine and married Amelia. It's an explanation but one where more research is required.
Good luck,
Frank