I can think of a 707 inbound to KJFK that ran out of fuel after much trouble along the way. And ATC not really understanding how bad things had gotten.
That was one of the accidents we studied at NTSB school. In additional to a communication problem, it was a cultural problem as well. The captain was not listening to the ATC communication, the First Officer was handling ATC.
When it became quite evident to the captain that they were in a critical fuel situation, he told the FO to declare a Mayday.
The First Officer did not.
Three times (so I recall) the captain asked the FO if he had done so*, the FO lied and told the captain he did.
By the time ATC realized that things were heading south, it was too late.
* The captain could not understand why they had not been immediately vectored toward the final approach path after declaring a Mayday, not knowing of course that no Mayday had been declared by the First Officer. If the First Officer had declared a Mayday when the captain ordered him to do so, it was determined that the aircraft would have landed safely. The fact that the captain was not monitoring the ATC communications was a contributing cause of the accident.