I don't think you can count on 3 years -- those numbers are used for estimates only during new applications.
Once approved, registries have to meet other financial requirements.
If a registry breaches their ICANN agreement for business or technical reasons, ICANN can force them to transfer data to another registry through the Registry Transition Process.
For gTLDs, an RFP is sent out for someone to take over the registry. If no RFPs are received or approved, then the gTLD will be closed in accordance with the gTLD's sunset rules.
The Continued Operations Instrument is used for new gTLD applicants only. This however is not guaranteed since estimates are used. New gTLD registries have to show 3 years of estimated operating expenses on hand to get approval.
I do not know exactly how these two policies fit together. I suspect that ICANN will attempt to transfer the name to another entity as soon as they can to assure continuity. If they cannot, then the COI can be used to operate the domain for as long as possible.
In addition, all registries are required to escrow their data with a third party. This assures that key whois and other information is not lost in case of a technical or business failure.