...but the input filehandle stopped at the original eof

Presumably just the usual Suffering from Buffering. Adding $fh_out->autoflush(1); (after having opened the output file) should make things behave as you expect (fill the file with letters up to 'z').  You also need to load IO::Handle for the autoflush method to be available — i.e. -MIO::Handle if you want to stick with your one-liner :)

BTW, there is nothing special with lexical filehandles in this regard, the piece of code would work just as well with normal filehandles like IN, OUT.