Firstly, to answer your question: What happens next?
Basically, the United Kingdom will continue to leave the European Union after 2 years of negotiation regardless of whether they get a deal.
However, this gives rise to another question: Whether the UK can "untrigger" Article 50 which I will discuss more below.
So, the main question here is if Article 50 can be "untriggered" or reversed.
Article 50 is vague and does not mention it. Basically, there wasn't any official mechanism to withdraw from the EU until the Lisbon Treaty in 2009. It was also never really meant to be used, so it may be unclear in some areas such as this.
Some articles that have mentioned this:
The Guardian - Only parliament can trigger Brexit. But can it then reverse the process?
This year, May might induce it to repeal the 1972 European Communities Act, but next year it might decide to repeal her great repeal act (2017), and to remain in Europe. Although this was not the view of the parties in the supreme court, it follows both from the judgment and from the language of article 50 itself, which tells a departing state that it “may decide in accordance with its own constitutional requirements”. So unless de-Brexit is blocked by European states fed up with the UK by this stage, it would be possible for a future parliament to decide to withdraw from the Brexiting process.
The Independent - Brexit ruling: MPs 'could stop EU withdrawal even after Article 50 is triggered'
“In my view it is strongly arguable that triggering Article 50 is not irrevocable and that Parliament can decide to withdrawn from Brexit before the process is complete.
“A future Parliament can decide to stop the Brexit process in its tracks simply by repealing any act or any statute that the Government, as a result of today’s decision, manages to pass.”
Article 50 itself says a state’s departure from the EU must be done in accordance with its constitutional laws.
Politics.co.uk - Can we withdraw Article 50 once we trigger it? Probably (but it's complicated)
However, Article 50 is not very well written. There is no explicit provision for this. Equally there is no precedent for withdrawing from the European Union, so there is little to go on. Jan Komarek, a lecturer at the London School of Economics' European Institute and Department of Law, says that, as Article 50 is "silent" on whether a withdrawing member state could change its mind during the negotiation period, lawyers would have to look for other examples in international law. Under the Vienna Convention, for example, a "fundamental change of circumstances" is grounds for withdrawing from an international agreement, provided "the existence of those circumstances constituted an essential basis of the consent of the parties to be bound by the treaty".
In other words, if the UK no longer consents to being part of the EU, it may leave the EU. If that situation changes and the UK decides to remain, it may remain. "When a state which is party to an international agreement wants to revoke the agreement and then wants to revoke the revocation of the agreement, that is possible according to the Vienna Convention," Komarek says.
So, in conclusion, it's still unclear if the UK can withdraw its notification to trigger Article 50. That being said, it's also unclear at this stage to see how the negotiations with the EU will result and how would the UK Parliament vote on the Brexit deal if they get the chance to.