In "TNG: The Best of Both Worlds," 40 Starfleet starships under the command of Admiral J.P. Hanson gather near Wolf 359 to intercept a Borg cube ship traveling to Earth. (The Star Trek Encyclopedia (1999), by Mike Okuda, Denise Okuda, and Debbie Mirek)
From (TNG: "The Best of Both Worlds, Part II"):
RIKER: The Enterprise'll be there, sir. Maybe a little late, but we'll be there, sir.
HANSON [on monitor]: Your engagements have given us valuable time. We've mobilised a fleet of forty starships at Wolf three five nine, and that's just for starters. The Klingons are sending warships. Hell, we've even thought about opening communications with the Romulans.*
According to dialog in "TNG: The Drumhead," 39 ships are destroyed.
SATIE: Tell me, Captain, have you completely recovered from your experience with the Borg?
PICARD: Yes, I have completely recovered.
SATIE: It must have been awful for you, actually becoming one of them, being forced to use your vast knowledge of Starfleet operations to aid the Borg. Just how many of our ships were lost? Thirty nine? And a loss of life, I believe, measured at nearly eleven thousand. One wonders how you can sleep at night, having caused so much destruction. I question your actions, Captain. I question your choices. I question your loyalty.
I don't remember hearing of a ship surviving or anyone discussing it, but I just did the math.
From (TNG: "The Best of Both Worlds, Part II"):
RIKER: Slow to impulse. Take us to the battle coordinates, Mister Crusher. Yellow alert.
WORF: Sensors are picking up several vessels, Captain.
RIKER: The fleet?
DATA: No active subspace fields. Negligible power readings.
RIKER: Life signs?
DATA: Negative, sir.
WORF: Visual contact.
RIKER: On screen.
By the time that the Enterprise arrived, there were no life signs or power readings from the remaining hulls. So it appears none of the ships survived, unless one fled during the battle... but we still have the math 40-39=1.
What was the name of the one ship that survived the battle? What happened to it? Why did it survive? How did it survive? Did any of the crew aboard the surviving ship survive?