#+NAME: print
#+begin_src emacs-lisp :var data=""
(print data)
#+end_src

Double quotes are preserved as long as there is no double quote as
first character:
#+NAME: ex1
| a"     |

Sourrounding double quotes are stripped:
#+NAME: ex2
| "a" |

#+CALL: print(data=ex2)

#+RESULTS:
| a |

This is unexpected:
#+NAME: ex2b
| "this_stays"this_has_to_go |

#+CALL: print(data=ex2b)

#+RESULTS:
| this_stays |

(Unpaired) double quote at beginning results in "End of file during
parsing":
#+NAME: ex3
| " |

#+CALL: print(data=ex3)

Passing an argument with (unpaired) double quote as first character to
code blocks works...
#+NAME: ex-code1
#+begin_src emacs-lisp
'("\"")
#+end_src

#+CALL: print(data=ex-code1)

#+RESULTS:
| " |

... as long as it's not from a cached result.
#+NAME: ex-code3
#+begin_src emacs-lisp :cache yes
'("\"")
#+end_src

#+RESULTS[f8bc0a680e2f0b8e579b262a13747cef1522cd72]: ex-code3
| " |

This results in "End of file during parsing":
#+CALL: print(data=ex-code3)