Don’t line break between a number expressed in digits and the noun it applies to. Don’t line break at an abbreviation that has a period at the end of it, or they will think it is the end of the sentence.
I don't know if this is the official term for it, but I found many results on Google images for the terms graph break and break symbol. break A zigzag on the line of the x- or y-axis in a line or a bar graph indicating that the data being displayed does not include all of the values that exist on the number line being used. Also called a Squiggle. - Mainland High School, Vocabulary reference ...
Many do not permit a double break--for example, putting "self-support-" on one line and "ing" on the next. Many computers programs do permit this, however, and editors often go into a file to manually override such a break. This has nothing to do with content or meaning or the reader's understanding--it is simply an aesthetic preference.
A comma immediately follows a word; that is, there is no space between the word prior to a comma and the comma itself. Just as you wouldn't randomly divide a word in half because of a line break (unless indicated with a hyphen), you wouldn't separate the word and the comma that follows it. They should stay together, on the same line.
But Chicago doesn't address paragraph break omissions at all. The closest it comes to such stronger breaks relates to a situation involving perhaps too strong a break: the whole-line space between stanzas in a poem. Chicago 16 addresses this subject at 13.32: 13.32 Running in more than one stanza of poetry.