Not really. Even with a monolith, you get partial availability. Most often as a default.
Imagine a web server handling requests. It usually has a way to recover from a crashed request handler. On top of that, you have multiple web servers behind a load balancer. Some code paths may be failing, some may be available.
Then, you have some background workers, maybe ingesting data from third party services. They're completely different processes from your web servers, even though they still use the monolithic code base. If they're down, the web app can still work with stale data.
The partial availability can be compromised in microservices as well as in a monolith (e.g. auth as you mentioned).