Assume you have copied a file across the network using something like this:
scp host:/path/to/file .
Then assume something goes wrong, so the transfer is interrupted. To continue the transfer, do this:
rsync --partial host:/path/to/file .
(Or, rather, always use rsync as above when transferring very large files.)
(Also note: I don't know how frequently rsync flushes its buffer, but don't assume something is wrong just because the file you're downloading doesn't increase in size in the file system. When you interrupt rsync using Ctrl-C, it will flush its buffers.)