I did find the Pierce's in Ashland on the 1910, but no sign of the Harrisons.
Here's the Pierces: Oregon, JACKSON, Roll 1281 Book 2, Page 282a 2ward Ashland
Looks like 243 Helman St
Pierce, Charles Head/age 48/married once/married for 17 years/NY/NY/NY/Proprietor Cannery Pierce, LauraWife/age 36/married once/0 children born-0 living/MO/Mississippi/Mississippi
They were all together on the 1900- Oregon, Jackson County, Page 256 East Medford Precint
Pierce, Chas. H. Head/born Feb 1864/age 35/Married 7 years/NY/NY/Conneticut/Lumberman Pierce, Laura GWife/born Jan 1874/age 26/married 7 years/0children/MO/England/MO/ Harrison, Helena A Mother-in-law/born Oct 1857/age 42/married 28 years/3 children born-3 living/Michigan/GA/Michigan Harrison, Harry Brother-in-law/born Feb 1883/age 17/Colarado/Nova Scotia/Michigan/attends school Harrison, Newsome Brother-in-law/born Aug 1886/age 13/Oregon/Nova Scotia/Michigan/attends school
So it looks like maybe the father is just missing-because she is continually listed as married. You should get her death certificate and see what it says about her husband. Also-there is probably an obituary for her-which should list some information.
She had an estate when she passed away-here's that record: Case#4579 NameHarrison, Helena A. Date12-31-1924 Record TypeEstate CountyJackson