Say someone wrote this sentence:
I like my co-
workers.
But I'm not sure whether the author meant to write "co-workers" (hard hyphen) or "coworkers" (soft hyphen added only for a line break).
Then should I quote the above sentence as
(Similar but distinct question: When quoting, must I also copy hyphens used to divide words that continue on the next line?)
Only indicate linebreaks when you cite poetry or ancient texts written in lines. When citing contemporary prose, ambiguous end-of-line hyphens should be clarified.
If typographic conventions are important (e.g. in a critical edition of a text), inquire with the author, if possible.
If asking the author is impossible or excessive, check if the text contains the word not across a line break to find out how the author writes it, with or without hard hyphen.
If the text doesn't contain an unbroken occurence of the word, check other texts by the author.
If no other texts by the author are available or they do not contain that word, try to figure out which variant of English the author writes and use the form correct or more common in that variant (e.g. British English seems to prefer co-worker while American English seems to prefer coworker, but that is just my hunch, make sure you properly research this).
If neither approach leads to a solution, randomly choose one variant.
As in other situations where you're quoting a text that contains potentially confusing or ambiguous elements, such as typos or misprints, or an unusual word, a common device that can be used to alert your readers to the issue and avoid the need to guess or interpret the quoted author's intent is the use of the adverb "sic".
In the current example, if you are unable to discern whether the author meant "co-workers" or "coworkers", you can quote the text as
I like my co-workers. [sic]
As @Ben's answer discusses, sometimes it is possible to fathom the author's original intent by contacting them or by studying the text for various clues that inform how to resolve the ambiguity. It's fine to do that in the current context, for example by following steps 1-4 in Ben's answer. But the "sic" device makes it unnecessary, or can at least be used as a last resort if other options fail.
The "sic" option also puts the emphasis on the fidelity of the quote. In a small and symbolic way it promotes truthfulness and accuracy, in a way that tossing a coin — the other answer's suggested last resort-solution — does not.
