Escape attempts at Elmira seemed to be fairly common from what I find. One account describes the punishment for prisoners caught in escape attempts, and implies that tunneling was a common way to wind up there.
The majority of escape attempts led not to freedom, but rather to an
escorted walk to the guardhouse. The building, which measured
forty-five-by-eighty-by-twelve feet, was divided into cells for
solitary confinement. When an offender was taken inside, he was
brought down the row of cells and usually imprisoned alone. After the
door slammed shut, it was locked, the diamond window closed, and there
one remained for hours, days, and perhaps weeks, isolated in the dark.
Meals were bland, restricted to soup and bread. Elmira inmates dubbed
the cells the "dungeon", but Wilbur Grambling's two day "trial" in the
guardhouse was long enough for him to think of another name: a "pretty
lousy hole." Tunnelers occupied many cells. Empathetic guards referred
to them as the "Engineer Corps," not resenting them as much as those
jailed for stealing, fighting, and disobeying prison rules.1
In fact, the number of escape attempts (or possibly the perception) motivated the camp administration to place an under cover informer amongst the ranks of the Confederate prisoners held in the camp. This, along with a system of trusties, would seem to have been pretty effective at limiting the number of successful escape attempts.
Conditions in Elmira motivated great numbers of Confederate prisoners
of war to consider the possibility of escape. Attempts at escape,
sometimes on the verge of being hatched, were almost always aborted by
a spy system that had successfully infiltrated the prisoners' ranks. A
network of so-called Confederate "oathtakers" and a chief
informant--Melvin Mott Conklin, a Union soldier from Owasco, New
York--served the prison administrators well in detecting various
escape schemes. Conklin, a young man who would marry and settle in
Elmira and serve for many years as the city's postmaster, posed as a
prisoner of war inside the camp.2
Conklin's experiences at the camp were relayed to the author of one of the first (or possibly the first) histories of Elmira's stint as a P.O.W. camp. In his interviews he describes constant and multiple attempts to tunnel out of the camp until shortly after the "great escape". The book is out of copyright, and is freely available on-line.
The first tunnel I found was started under Hospital No. 1. The floor
was about two feet above the ground. The tunnel was started near the
rear of the building toward the fence. The men worked nights. In the
daytime they covered up the hole with boards and put sod on top. I
found it and reported it. My orders were to let the men dig. I went
into the tunnel every day to see how it was progressing. When it was
about completed, an extra guard was located at night near where it was
expected to open out. The night they chose for escape happened to be a
bright moonlight night. When they broke through and the first
"Johnnie" stuck his head up he discovered, much to his surprise, that
he was right in the midst of the guard camp, with a dozen guards
looking right at him. He dodged back, but before the "Johnnies" could
get back to the other end of the tunnel I was there with the guards,
and we received them as they dejectedly came out. This was the time
Crawford was caught. Very soon another tunnel was discovered under
Hospital No. 2. I crawled into that one and found the paper with W. B.
Traweek's name on it, which sent him to the guard-house, as related in
his story. Soon another was discovered in the lower end of the camp in
the northeast comer. The occupants of the tent built a chimney at the
rear of the tent, and then tunnelled down from the inside of the
chimney. This one was directed northward and would have come out very
near where Ed Warner's grocery now stands near Hoffman creek. There
were two started in the tents on the flat near the fence, next to the
river, and two started in the barracks next to the east fence, about
half-way between Water Street and the pond. The most of the tunnelling
was on the east side of the camp, and some one was digging nearly all
the time during the fall of 1864. All being discovered, they finally
became discouraged and none were attempted after November.3
This book would be a good starting point for other first hand accounts of both successful and unsuccessful escape attempts.
Other resources to check would be the extensive (and also freely available) compendium The War of the Rebellion: a Compilation of the Official Records of the Union and Confederate Armies, particularly the second series specific to prisoner of war documents.
Another place to check would be the National Archives, which has two archives that appear promising - Records of Confederates in Union Prisons, compiled ca. 1865 - ca. 1899, documenting the period 1861 - 1865 and Registers of Confederate Prisoners, compiled 1889 - 1904, documenting the period 1863 - 1865.
Finally, you can always comb through period newspapers from the area.
1Gray, Michael P. The Business of Captivity: Elmira and Its Civil War Prison, p 124
2Horigan, Michael. Elmira: Death Camp of the North, p 105-6
3Holmes, Clay W. The Elmira Prison Camp: A History of the Military Prison at Elmira, N.Y, p 161-2