I don't know whether there are any text editors which keep the file opened while you are editing it. Normally (i.e. in Emacs), the file is read into a buffer in RAM and then the file is closed. You edit only in RAM. When you save the buffer, the file is opened, written, and closed again. You can use ps auxw | grep your_editor to find the PID of your editor, then lsof -p your_PID to see the files that are still open.

On the other hand, if the file is still in the buffer of your editor, you can just save it.

But that was not your question, so let's pretend you are using cat as your editor, and the file is really still open:

% cat >the_file.txt

Hello world!

^Z

zsh: suspended  cat > the_file.txt

% rm the_file.txt 

% ls -l the_file.txt

ls: cannot access the_file.txt: No such file or directory

You can use lsof -n to see all opened files and grep to search for your filename.

% lsof -n | grep the_file.txt

cat  2145  elmicha  1w  REG  9,1  13 108003357 /home/elmicha/tmp/the_file.txt (deleted)

In the second column you can see the PID of your cat command. You can change into the corresponding directory in the /proc filesystem, and into the fd (file descriptor) subdirectory:

% cd /proc/2145/fd

% ls -l

total 0

lrwx------ 1 elmicha elmicha 64 2012-11-07 00:22 0 -> /dev/pts/4

l-wx------ 1 elmicha elmicha 64 2012-11-07 00:22 1 -> /home/elmicha/tmp/the_file.txt (deleted)

lr-x------ 1 elmicha elmicha 64 2012-11-07 00:22 15 -> /proc/4501/auxv

lrwx------ 1 elmicha elmicha 64 2012-11-07 00:22 2 -> /dev/pts/4

Now you can just copy the "file" 1 to another file:

% cp 1 ~/tmp/the_old_file.txt

And see, it's there:

% cat ~/tmp/the_old_file.txt

Hello world!