There are many solutions to image old floppies on a very low, flux based level: Kryoflux, Catweasel, Fluxengine or Supercard Pro, to name a few. The Greaseweazle is a low cost, open source variant that can be had for less than 10 EUR. It is suitable to generate disk images of a wide variety of formats, including but not limited to IBM PC, Atari ST, C64 and Amiga. In this video you can see me test the device and create a pipeline for more or less easy creation of different disk images. In theory you can even salvage data off of damaged disks. This heavily depends on how much of the disk is still readable though, and you should weigh your options carefully if the data in question is really valuable, of course.