727 APU could not be started in-flight....
....but it would run if left on for takeoff and if somehow not noticed could result in a wheel well fire indication on climb out.
Years ago in TXL we had a young FE who forgot to turn off the APU not once, but twice. He was advised that his career prospects were limited and that he should seek employment elsewhere.
He got on with a cargo airline in MEM and did well. Sadly, he passed away a couple of years ago...