Ah, I see.
Breaking a word in two at a line break is neither unnatural nor unusual. In Japanese, there are no rules against it.
However, while it is not syntactically incorrect, there is a short list of characters that it is considered bad form to start or end a line with. It's a very small list for both, though.
In the example you gave, breaking the word just before the small version of イ is considered bad form, so your example should be changed to include the some other character before the small イ on the next line, as you have done.
For the most part, though, breaking a word in two at a line break is perfectly natural Japanese.
Here's a brief explanation in English.
3.1.7 Characters Not Starting a Line
In principle, no line should begin with closing brackets (cl-02), hyphens (cl-03), dividing punctuation marks (cl-04), middle dots (cl-05), full stops (cl-06), commas (cl-07), iteration marks (cl-09), a prolonged sound mark (cl-10), small kana (cl-11) or warichu closing brackets (cl-29) (line-start prohibition rule). Otherwise the line would have an odd appearance.
Not a small number of books adopt a less strict set of rules which allow IDEOGRAPHIC ITERATION MARK "々" (one of the iteration marks (cl-09)), prolonged sound mark (cl-10) and small kana (cl-11) to start a line. There is another method whereby IDEOGRAPHIC ITERATION MARK "々" is replaced by a kanji character when it would otherwise be set at the head of a line. For example, 家 (at the end of a line) + 々 (at the head of the next line) will be changed to 家 (at the end of a line) + 家 (at the head of the next line).
There is yet another less strict rule that allows KATAKANA MIDDLE DOT "・" to start a line.
In the layout of newspaper text, dividing punctuation marks (cl-04) (QUESTION MARK "?" and EXCLAMATION MARK "!") are allowed to start a line. This is due to the fact that the line lengths are shorter in newspapers. When the line is very short, there are fewer opportunities for inter-character space adjustment, which makes it difficult to preserve the number of characters per line. It is thought that this is the reason why the less strict set of line head wrapping rules was adopted in newspaper text layout.
The details of the line-start prohibition rules and line-end prohibition rules are described in Appendix B Spacing between Characters as a complete table, following the description of character classes in 3.9 About Character Classes.
3.1.8 Characters Not Ending a Line
No line should end with opening brackets (cl-01) or warichu opening brackets (cl-28) (line-end prohibition rules). Otherwise the line would have an odd appearance.
The process of formatting lines to avoid non-starter characters at the line head, non-ending characters at the line end, spaces before and/or after inseparable characters, line breaking before and/or after unbreakable characters, etc., is generally called kinsokushori.
[Edited at 2015-04-07 18:37 GMT]
[Edited at 2015-04-07 18:58 GMT]
[Edited at 2015-04-07 19:02 GMT]