If you're using the cloud service directly, it's possible. But with the edge agent, all access checks will continue to function even if the cloud service is hard-down.
And as others have mentioned, we're also planning to offer on-prem/private cloud deployments in which case the entire stack would live on customer infra.
Like Akajla said, a local Policy Decision Point (PDP) can solve outages really well.
An open-source event-driven engine like OPA+OPAL which can keep the PDP up to date is an easy way to approach this in scale (that's what we use as part of Permit.io)
And as others have mentioned, we're also planning to offer on-prem/private cloud deployments in which case the entire stack would live on customer infra.