Likely, they can refuse delivery and pay nothing as you did not deliver what the contract specified. Those details may in fact be in the contract already. Pro

Likely, they can refuse delivery and pay nothing as you did not deliver what the contract specified. Those details may in fact be in the contract already. Probably best to see what you actually agreed to. However, it sounds like they want the piece you did deliver. It seams reasonable to me that they would pay for whatever percentage you completed. That is assuming you can agree on what that percentage is. My guess is that your estimate of completion may not align with their's. Your financials may not allow it, but if it was me, I would give them a steep discount in order to maintain a good relationship with them. Then I would try to negotiate the potential of delivering the missing functionality in the future.