Sadly John and Mary Ann did not have a happy marriage and conflict between them led to the unfortunate circumstances that lead to both their deaths. Newspaper reports from the time describe in graphic detail how John killed his wife and then took his own life. 
On 6 April 1859 the Derby Mercury reported on the inquest of Mary Ann. 
THE MURDER IN STAFFORDSHIRE. - An inquest upon the body of Mrs. Corbett, whose brutal murder by her husband we reported last week, has been held at West Bromwich, and terminated in Corbett's committal for "Wilful murder." The murderer, however, will be little affected by this verdict, the surgeon having declared it impossible that he could live. In cutting his throat he has divided the windpipe and touched the neck bone.
John passed away a few days after the death of Mary Ann in 1859.  He was buried on 25 May 1859. 
The Manchester Courier of 6 April 1859 reports on an inquest on John:
THE MURDER AT WESTBROMWICH, - On Wednesday an inquest was held at West Bromwich on John Corbett, the miner, who, it will be remembered, after murdering his wife in that town on the night of the 25th of last month, cut his own throat in a most dreadful manner, using for the purpose the knife with which he had just before taken his wife's life. Against Corbett the coroner's jury who investigated the cause of his wife's death returned a verdict of wilful murder. He was then lying at the house of a relative, and was not removed to gaol, but police-offices tended upon him night and day as his nurses until the time of his death, which occurred on Tuesday. The surgeon, Mr. W. J. Kite, after reading the depositions, was decidedly of the opinion that Corbett, when he cut his wife's and his own throat, was not insane; on the contrary, he thought that the evidence of what he did before the murder, and his attempts to strangle himself afterwards, showed that he was a determined suicide. Evidence was then given to show that four days before the murder he showed his wife, at midnight, a large knife, saying, "Do you see this" and adding, "we have both got to die." The jury, first, after some considerable consultation, were (being 14 in number) 10 for a verdict of felo de se, and four for one of insanity; after calling in the aid of the coroner, however, they decided 13 for the former verdict and one for the latter.
John Corbett - 16 - Son - Coal Miner - Tipton, Staffordshire
Eliza Corbett - 10 - Daughter - West Bromwich, Staffordshire
Jemimal Corbett -10 - Daughter - West Bromwich, Staffordshire
Deborah Corbett - 6 - Daughter - West Bromwich, Staffordshire
Luke Corbett - 4 - Son - Scholar - West Bromwich, Staffordshire
Lucy Corbett - 2 - Daughter - West Bromwich, Staffordshire
John Bridgewater - 15 - Son in Law - Coal Miner - Dudley Worcestershire
↑ IGI, "England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JQPY-57J : 30 December 2014), John Corbett, 08 Mar 1835; citing TIPTON,STAFFORD,ENGLAND, reference ; FHL microfilm 435,872, 435,873, 435,874.
↑ "England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J9G2-R45 : 6 December 2014, John Corbett, ); citing St. Martin's, Tipton, Stafford, England, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,526,134.
↑ 3.03.1 UK census 1841 - West Bromwich, Staffordshire
↑ 4.04.1 UK census 1851 - Dartmouth Street, West Bromwich, Staffordshire
↑ "England and Wales Marriage Registration Index, 1837-2005," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2DSK-N5Q : 13 December 2014), John Corbett, 1854; from “England & Wales Marriages, 1837-2005,” database, findmypast (http://www.findmypast.com : 2012); citing 1854, quarter 2, vol. 6B, p. 824, West Bromwich, Staffordshire, England, General Register Office, Southport, England.
↑ GRO index (Deaths) - CORBETT, JOHN 24 GRO Reference: 1859 J Quarter in WEST BROMWICH Volume 06B Page 419.
↑ "England Deaths and Burials, 1538-1991," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J8H6-V53 : 24 December 2014), John Corbett, burial 25 May 1859; citing , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,042,394.
It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share DNA with John: