Theoretical answer: The cars would continue to function as cars, but network-dependent features like Autopilot and remote unlocking/monitoring would cease.
now I did not need to use a super charger but one would hope they don't need network access to work and would just keep a local database of cars that are allowed. would be damn silly to require a call to the mothership for each charging session.
With the key card?
https://www.tesla.com/autopilot
> Tesla’s Enhanced Autopilot software has begun rolling out and features will continue to be introduced as validation is completed, subject to regulatory approval.
Funding secured
It's going to Chapter 7 - Liquidation.
http://www.uscourts.gov/services-forms/bankruptcy/bankruptcy...
There is virtually no question that the Supercharger network will be bought by someone in the event of Tesla going under -- another car company, or another company that already operates a charging network, or even a new company formed to run the network. The new owner would almost certainly open it up to non-Tesla customers if that's at all possible, too. I don't think this is just true of this network, either; I have little doubt that all of Tesla will be bought if they collapse, although they might be broken up and bought piecemeal.
If I was forced to make a prediction for Tesla's fate, though, this wouldn't be it. I think it's most likely that Tesla will be bought in total by another carmaker within four years, and it will continue as a semi-independent brand for years past that, with its technology being diffused through the rest of their new owner's properties -- and vice-versa.
But, it begs a question about such system in the long-term. If we look at the electric car segment of all transport, as it replaces ICEs over time - the systems they rely on to function are bigger than a single brand.
No. There may be some enormously expensive, 3rd party service that springs up to fill demand for custom fixes with the machines, but warranty holders get nothing if the company goes bankrupt and dissolves liabilities.