Now that the goal has been clarified:
I have a 1979 Exidy Sorcerer 8 bit computer with a parallel port. I wanted to find a way to make it talk to a USB flash device, but as pointed out in the comments and answers, it's just not possible to drive the parallel port signals to control the USB device. I'll look for an alternative solution.
There's an awkward solution to your real problem, a clean one, and a software one. Both the hardware options require that you can manipulate individual bits in the parallel port, and not merely send synchronous words to a printer.
First, you could get an SPI to USB Host bridge, probably most practically one sold as an add-on sold for Arduino boards. You would then need to bit-bang SPI using four or so pins of the parallel port's data word, and have software to operate the bridge chip to perform USB mass storage operations, and finally you'd have to implement a file system. This comes closest to your original idea of using a USB-to-Parallel cable, but with hardware actually intended to work in the reverse direction as you require, which as others have explained is something those limited purpose cables cannot do.
A much cleaner option would be to replace the USB flash drive with an SD card which you could operate in legacy MMC-SPI mode (and which modern systems can use via a USB card adapter). Here you are basically just bit-banging a slightly odd SPI peripheral. You would need to then speak MMC commands, and finally implement a file system (unless you want to treat the card as a raw block store). This is pretty commonly done to give legacy computers "a hard disk" so you may well be able to find software for a compatible enough processor/system to jump start an effort.
Finally you could implement effectively a network file system, by using some available interface like a serial port to communicate with a modern system (PC, Raspberry Pi, whatever) that functions as a semi-custom fileserver. With care this can probably be made to have the smallest software footprint on the legacy system, since you can customize the scheme to make the task easy for that end.
Or if you don't mind a painfully slow solution, you could probably make a PC soundcard function as a virtual cassette tape, as your system seems to have an interface for that. This may well be the only path that does not require you to delve deep into operating system internals of the legacy system.