In the late 1960s or early 1970s I read a short story in an anthology of science fiction stories borrowed from the library. The story concerned the complete alien occupation of Earth by an alien culture who used humans as work slaves. They had the ability to enable the humans to keep going on and on using enhancements to keep them strong and alive. Life was suffering and unremitting work for a man who submitted a request through "channels"--to be allowed to die. He was informed that he already had a request pending--for a new winter coat and must make a choice, for one or the other. The story haunted me, and I've been trying to locate it ever since.
Fifty years after the arrival of aliens, one of the small percentage of men left alive enters the alien bureaucracy dreaming of a new overcoat -- or better yet, escape.
I don't have a copy of the story and I can find only very fragmented quotes by searching through Google Books, but there's enough that's suggestive, at the very least (the paragraphs below are not necessarily directly connected):
"Name Roger Freeman. Number 655-673-60-60-2. You have a single time application outstanding. Unpermitted two. You will cancel this one. Or you will cancel that one."
Frantically he searched his mind. What application did he have outstanding? When was this rule made? The overcoat! If he went ahead with this new application and it was refused he'd have to wait till next year to reinstate the one for the coat. And then more years of waiting . . . It was cold, the dormitory was ill-heated, and he had no blanket. His present coat was very worn. Services for humans were minimal.
[. . . .]
A piece of paper slid from the machine. He took it up, waiting for the command to proceed—where? Unless it could be accomplished before ten, there was no chance of escape for him this year. None whatever. He stared dully at the strange characters. The cold indifferent voice said, "Name Roger Freeman. Number 655-673-60-60-2. Declared surplus. Application for death certificate is granted. Proceed for certificate to Office One, Level Five. At once."
If you read it in the 60s or early 70s, it was probably in A Decade of Fantasy and Science Fiction from a variety of authors, or Strange Seas and Shores, a collection of Avram Davidson's work alone.