On January 30, 1900, Democrat William Goebel was shot while the results of the previous year's election for Governor of Kentucky was still being contested; Goebel was declared the winner, and died shortly afterwards.[2] Finley was one of several Republicans suspected of involvement; they were indicted, and arrest warrants were issued.[2] Along with several others, Finley fled to Indiana to escape prosecution.[2] The Republican governor there refused to honor extradition requests, and they continued to reside in Indiana while the case was litigated.[2]
In 1909, Kentucky Governor Augustus E. Willson extended clemency to Finley and other suspects; they never faced trial, and then returned to Kentucky.[2]
Other service
Finley was chairman of the Republican executive committee of the Eleventh Kentucky Congressional District from 1912 to 1928.[1] He was elected as a Republican to the Seventy-first Congress to fill the vacancy caused by the resignation of John M. Robsion and was reelected to the Seventy-second Congress and served from February 15, 1930, to March 3, 1933.[1] He was not a candidate for renomination in 1932.[1]
After leaving Congress, he retired from business activities before dying in Williamsburg, Kentucky in 1941.[3] He was buried in Highland Cemetery, Williamsburg, Kentucky.[1]