A few things happen:
- They get downvoted a lot.
- Their material might be irredeemably low quality and deleted, or the answerer might delete it themselves. The rest sits around, accumulating downvotes, or serving as an equivalent of skulls on the ramparts letting people know what kind of quality doesn't fly.
- Eventually, they will probably get answer banned, and become totally unable to leave new answers.
That last one is a completely automatic mechanism. (There's also question banning.) It happens after making a lot of low quality posts. If your answers are getting downvoted or deleted, that counts towards an answer ban - same goes for questions and question bans.
Most users who contribute at all decently will never have to worry about either kind of ban. You have to provide a lot of consistently low-quality answers before you get answer banned, and that will be a significant portion of your answers. You can probably guess where this is going for this user.
The exact mechanisms of question/answer bans are kept secret by the SE staff so that they can't be gamed.
The user has an opportunity to get their ban lifted, if they work at producing quality material: doing good edits, posting good questions, etc. If they can't do that, or they post low quality questions, they might dig themselves an even deeper hole.
(There's a project in the works to redesign or replace Q&A bans, because extremely low-quality contributors can reach a point where they cease to care about bans and post quality completely, and re-register new accounts to post even more, meaning the system has a threshold at which it implodes and completely stops working.)