Backups of bootable floppy disks should be done by imaging the entire disk (creating what is essentially an .iso file...minus the ISO9660 part) – RawWrite was a popular Windows tool in the past. If you can boot Linux on the PC, cp
or dd
or ddrescue
would work (there's a version of dd for Windows as well).
Before UEFI, a critical part of making a bootable disk wasn't actually any specific file nor any specific partition – it was a "boot sector" that existed outside any partitions. Specifically sector 0 of the disk (known as the MBR) holds the initial boot code of any BIOS-compatible disk and is not visible as a file – it must be copied sector-by-sector, e.g. using disk imaging tools.
(Those "NTLDR" or "BOOTMGR" files that you might've seen on Windows disks – or the equivalent "IO.SYS" on MS-DOS – aren't the MBR; they're the 3rd stage after the MBR and VBR. Only UEFI brought to PCs the practice of having the system firmware directly load a specific file.)
Typically the only task of the MBR is to jump to a specific partition's "volume boot record" (VBR), which also is almost never visible as an actual file but must be copied sector-wise. But there are exceptions to this, e.g. GRUB doesn't go in the VBR. Floppy disks (being unpartitioned), are also different; their sector 0 directly holds the specific boot code.
So for some disks you may be able to write a generic MBR (and VBR where applicable), e.g. using the MS-DOS sys
command (the .SYS and .COM files look extremely like MS-DOS), but that's not guaranteed to work even if you use the correct version.1
You'd also need to make sure that the new disk is formatted in the correct file system; a boot sector that understands how to boot from a FAT12 disk will not necessarily understand FAT16 or FAT32, much less NTFS or exFAT. (And if the boot sector does, the booted OS may still not – you can't boot MS-DOS from an exFAT filesystem without major hacks.)
So in short, it'll be easiest to just create a whole-disk image and write it to the USB stick. (Once you have the .img file, you can also give it to any VM software to use as a virtual floppy disk.)
This also leaves out the fact that even if you create a perfect backup on a USB stick, modern-day PCs might not even support the BIOS-style boot process anymore or at least have it disabled by default (the "CSM" option in firmware settings).
1 (Side note: For modern Windows systems, bootsect
is the similar command – making a BIOS-bootable Windows installation USB stick involves copying the files and writing a standard Windows MBR & VBR using bootsect.)