Cossen’s parentage is unknown, but he probably belonged to the family of that name found at St. Ives and elsewhere in west Cornwall.
Cossen made his will on 12 Oct. 1619, its bequests including the provision of funds for an annual loan of £6 to local young men, presumably for commercial purposes. The interest accrued from the loan, which was to be administered by the Truro corporation, was partly intended to fund an annual sermon in the town, a godly objective which also found expression in the almost contemporaneous will of Cossen’s 1604 parliamentary partner, Thomas Burges I. Cossen left his younger sons legacies of up to £80, and his wife an annuity of £20 and selected household goods, including a ‘London bedstead’. He died a few weeks later, and was buried at Truro parish church on 7 November.
