@Mike Compton Password Hashsync allows the users to sign into cloud services irrespective of on-premise server status. IF a users password has been sync it is set to never expire in cloud and the user should be able to use the cloud service even when the on-prem DC is down.
Coming to your scenarios, there must have been other issues which might have caused the users for not being able to sign in.
As a preventive measure, you can try suggesting your users to use this keep me signed in box when signing in to the cloud services protected by Azure AD, This selection sets a session cookie that bypasses authentication for 180 days.
Read more here : https://learn.microsoft.com/en-us/azure/active-directory/hybrid/how-to-connect-password-hash-synchronization
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