Nir Lichtman pointed out that rm -p shouldn't try to rmdir / at the end.

tests/rmdir.test

@@ -40,6 +40,10 @@ testing "-p part of path" \
 	"yes\n" "" ""
 rm -rf temp
 
+skipnot [ $UID -eq 0 ]
+testing '-p abspath' \
+  'mkdir -p /test/2/3 && rmdir -p /test/2/3 && [ ! -e /test ] && echo yes' \
+  'yes\n' '' ''
 
 mkdir -p one/two/three
 testing "-p one/two/three" \

toys/posix/rmdir.c

@@ -25,7 +25,7 @@ static void do_rmdir(char *name)
 {
   char *temp;
 
-  for (;;) {
+  do {
     if (rmdir(name)) {
       if (!FLAG(ignore_fail_on_non_empty) || errno != ENOTEMPTY)
         perror_msg_raw(name);
@@ -39,7 +39,7 @@ static void do_rmdir(char *name)
       if (!(temp = strrchr(name, '/'))) return;
       *temp = 0;
     } while (!temp[1]);
-  }
+  } while (*name);
 }
 
 void rmdir_main(void)