Microsoft Account
Although it's harded to find official online documentation on this, it seems to work similarly as with the Active Directory domains described below. According to Microsoft Specialist Guide to Microsoft Windows 10 (Exam 70-697, Configuring Windows Devices) by Leon Plesniarski & Byron Wright:
Cached credentials are also used when you selct to sign in with a
Microsoft account in non-domain networks. Cached credentials for
Microsoft accounts ensure that you can sign in when your computer does
not hace access to the Internet.
Top Password Software, Inc. has this blog post that states (for Windows 8):
The cached logon credentials will never expire itself. If you change
your Microsoft account password online via https://login.live.com, the
cached logon credentials won’t update until you successfully log in to
Windows 8 with the new password. After you have successfully logged in
to Windows 8 with the new password, you cached logon credentials are
updated.
This seems quite reasonable: if the computer completely loses network connectivity (due to hardware failure or configuration error) and there's no local administrator accounts available, you'd completely lose your access to the operating system on password expiration. This also renders you unable to fix the network connection required for checking the new credentials over the Internet.
Despite the cache doesn't expire based on time limits it doesn't mean you can use all your previous passwords, as the new password will replace the previous during the first login with it. This way, a password change invalidates the old credentials; not just at the moment you expected it.
As, starting from Windows 8.1, Microsoft has disabled WDigest and enabled LSA Protection by default, it's less of a problem to store the credentials locally. More information e.g. on Preventing Mimikatz Attacks by Panagiotis Gkatziroulis.
Active Directory Domains
From Cached and Stored Credentials Technical Overview:
Windows logon cached password verifiers
These verifiers are not credentials because they cannot be presented
to another computer for authentication, and they can only be used to
locally verify a credential. They are stored in the registry on the
local computer and provide credentials validation when a domain-joined
computer cannot connect to AD DS during a user’s logon. These “cached
logons” or more specifically, cached domain account information, can
be managed using the security policy setting Interactive logon: Number
of previous logons to cache (in case domain controller is not
available).
A user can't use the old cached verifiers once
- the domain-joined computer has been able to contact a DC during a logon for the user, caching the new domain account information
- more users than specified in the "Number
of previous logons to cache" policy have logged in after the user.
However, there seems to be no time based limit for this cache to expire. You could set the number of users to zero, but then no-one would be able to login if there's no DC available. This would probably be ok for most in-office desktops, but not so good with laptops.