I believe you are talking about the Warensville Workhouse, located in what is now Highland Hills Ohio.The area was largely undeveloped until Figgie International proposed building its HQ there, which fell through.Office Max built its HQ on part of the property a few years ago but I believe that at least one building remains.
Here are some links which may help.
The Cleveland Workhouse and House of Refuge and Correction Records are a valuable source for the study of penology and charity in a major city, particularly during the Progressive Era. Originally intended as a place where petty lawbreakers could work at productive occupations to help pay their fines and court costs, the Workhouse eventually grew to include The House of Refuge and Corrections, a juvenile facility; and Cooley Farms, a penal farm colony, that included a tuberculosis sanatorium. The Workhouse was one of the leading progressive penal institutions in the country. Though principally related to the administration and functions of the Workhouse, some of the material in this collection relates to allied organizations, including the City Infirmary and the Department of Outdoor Relief.
One on-site building is a leftover from the Warrensville Workhouse that currently houses records from the City of Cleveland. Negotiations are underway for records removal and the demolishing of that structure.
Between 1904-15 progressive city and county institutions located in the present township: the County Infirmary (1904, now part of Highland View Hospital); the county tuberculosis sanatorium at Cooley Farms (1906, later the Sunny Acres Sanatarium, see CUYAHOGA COUNTY HOSPITAL SYSTEM (CCHS)); and the CLEVELAND WORKHOUSE and House of Correction (1912).