Floppy disks isn't the only option for data transfer to/from old 386'es:
There were CD readers even for old 386'es, which offered an option to
transfer files to, but not from, that 386.
A few years ago I decided I wanted to transfer all the contents of my
old 386 to CD and archive it there. Since I knew no way to add a CD
burner to that 386, all the files had to be transferred to a more
modern computer. I had 700 MBytes disk space on that 386, of which
some 600 MB actually was used, which meant that the contents would
nicely fill one CD. But I considered it impractical to transfer all
those 600 MBytes to another computer using floppy disks. The solution
was to equip that 386 with an Ethernet card and connect it to my home
network.>