I believe that the surname Shrove is a corruption of another name of Germanic origin. I've been unable to find any census records of Henry, his siblings and parents prior to the 1870 census.
Henry married Elizabeth FITSPATRIK [?], daughter of Unknown FITSPATRIK [?] and Catherine UNKNOWN, about 1835 in Pennsylvania. (Elizabeth FITSPATRIK [?] was born about 1814 in Pennsylvania and died in Prob. Illinois.)
1 1870 US Census (Loran, Stephenson County, Illinois). Repository: Ancestry. Surety: 4. Lists Henry Shrove (age 54, b. PA), wife Elizabeth (age 56, b. PA) and children Jeremiah (age 25, b. PA), David (age 17, b. IL) and Catherine (age 16, b. IL), living in Loran, Illinois. Also in the household are Catherine Fidapabrik [sp? May be Fitspatrik] (age 81, b. PA) [probably Elizabeth's mother] and Emma Shrove (age 3, b. IL) [grandchild, daughter of their son, Daniel]. Henry and Jeremiah are both listed as "farmers."
2 1880 US Census (District 180, Loran, Stephenson County, Illinois). Repository: Ancestry. Surety: 4. Lists Henry Shrove [spelled Shroff] (age 66, b. PA), wife Elizabeth (age 67, b. PA) and children Jeremiah (age 33, b. PA) and David (age 26, b. IL), living in Loran, Illinois. Also in the household are "granddaughter" Cornelia (age 6, b. IL), "grandson" Arthur (age 2, b. IL), "grandson" Charles (age 1, b. WI), and "servant" Amie Koch (age 17, b. IL) who is listed as a "hired girl." Henry is listed as a "farmer," and indicates that his parents' birthplace is "unknown." [Info probably provided by other family member]. Elizabeth indicates that both her parents were born in Germany. The grandchildren indicate that both their parents were born in Illinois, which leads us to conclude that their father must be either David Shrove or Franklin John Shrove. Their mother's whereabouts are unknown, and she is presumably dead. Amie indicates that both her parents were born in Germany.