AppleID accounts do not disappear - unless the account is deliberately permanently closed by its owner. As described, the iPad is associated with your Mother’s AppleID account. If the account has been formally closed, dire warnings of the consequences, prior to fully signing-out of the AppleID on devices, will have been seen prior to account closure.
If the AppleID credentials have been forgotten, your Mother should be able to recover them here:
https://iforgot.apple.com
To recover your credentials, you’ll need access to one of the following:
- Your primary email address mailbox that corresponds with your AppleID
- Any of the secondary/recovery email addresses that should be configured for your AppleID account
- Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID
Unless you AppleID account has not been fully/correctly configured, or has been seriously neglected, recovery of the AppleID and password should not be difficult.
More information about recovery of your AppleID:
If you forgot your Apple ID - Apple Support
More information about recovery of your AppleID password:
If you forgot your Apple ID password - Apple Support
When you recover access to your credentials, you would be well advised to log-in to your AppleID account from a web browser - and verify/update any email addresses and trusted telephone numbers:
https://appleid.apple.com