You can simply copy the (proc) file to a new location to recover it.
Remember: open files keep the contents present on disk until the controlling process exists or closes the filehandle.
Since you're actually accessing the file on disk your issues of storage contingency don't come into play -- it's all read back to you in proper file order.
But yes, files (and virtual files) on Linux are pretty slick.
I also remember being really excited learning about disk image files and the ways in which they can be manipulated. Including the options of creating filesystems on virtual disks, partitioning them, and them mounting those partitions, etc. First tried with bootable floppy distros, but I've played around with them in a bunch of contexts since.