How can Shadrach have lived his entire adult life in Clermont County and never have turned up in the census?!  Is he really the Shadrach buried in Clermont County?  Did he possibly die in 1818, not 1868 (i.e., was his tombstone mis-read or did someone make a typo)?

1a.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):

Corbin, Shadrach

Carns, Mary

16 Oct 1817

Clermont Co.

1b.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org):

Shadrach CORBIN Spouse: Mary KARNS Marriage: 16 Oct 1817, Clermont, Ohio Source: patron submission

Shadrach CORBIN Spouse: Mary HARRIS Marriage: 16 Oct 1817, Clermont, Ohio Source: Marriage Records, 1801-1910. Ohio. Probate Court (Clermont County)

One can see how KARNS might be read for HARRIS, and vice versa (i.e., a capital followed by six "bumps").  In checking the 1820 census of Clermont County, there are no KARNSes or CARNSes, but there are many HARRISes, so I'm going with HARRIS, which also happens to come from the most authoritative record (viz., the Clermont County Court marriage record).

2.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):  not found.

3.  Census Index:  U.S. Selected Counties, 1830 (Broderbund CD-315):  not found.

4.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  not found. 

5.  Census Index:  U.S. Selected Counties, 1850 (Broderbund CD-317):  not found.  The Shadrach CORBIN (wife, Mary Ann CLARK) in the 1850 census of Clermont Co., OH, is our subject's nephew. 

6.  AIS (Accelerated Index System) Census Index (online at Ancestry.com):  not found anywhere in any year, and I did a wildcard search on "Shad* Corb*".  The only Shadrach CORBIN was our subject's nephew, in 1850 and 1860 in Clermont Co., OH; one in York Co., PA in 1810; and one in Huntingdon Co., PA, in 1830.