Has an NBA game ever ended 87-76?
It has. 87-76 has been a NBA final 19 times in 73,172 games. The first was Toronto Huskies beat Chicago Stags on December 31, 1946; the latest was Charlotte Hornets beat Detroit Pistons on February 10, 2020.
That makes 87-76 the 1001st most common final score out of 3,189 that have ever occurred in NBA. One point away, 88-76 has happened 22 times and 87-77 has happened 18 times. At one point the score disappeared for 35 years, between 1955 and 1990.