Apparently, it is possible to have a line break in one's signature. This should display a warning on the preferences page or be disallowed (similar to https://www.mediawiki.org/wiki/New_requirements_for_user_signatures).
Line breaks in signatures are problematic because:
- Usually they will cause the markup to break when the signature is used in a nested comment (in a list item)
- When the line break is inside a link label, it does not break the markup, but it can cause dirty diffs in Parsoid (T265094) and can be confusing to people reading the wikitext and trying to reply
While you can't type them in the Special:Preferences interface, because it has a single-line text field, you can such a signature via an API or by using a substituted template in your signature.