What options would have been left, if the UK government couldn't have decided on how exactly to implement the referendum to leave the EU?

To my understanding, the lawful government of the United Kingdom has decided, following due process, that:

• The United Kingdom shall leave the European Union at a set date (currently 29 Mar 2019)
• The United Kingdom shall not accept the deal negotiated with EU27
• The United Kingdom shall not leave the European Union without a deal

Given that, what happens when the set date arrives (whether that is 29 Mar, or an extension is applied for and granted)?

Can EU27 simply assume that "Since your Parliament ruled out both the negotiated deal and a hard Brexit, we assume that all treaties are still valid."?

Can EU27 simply assume that "Since you did trigger Article 50 and declined the negotiated deal, we (regretfully) assume that all treaties now are void"?

EU27 are supposed to honor the decisions of UK's legal government, but what are the options if the stance of that government is literally "we cannot decide"?