If a server-side password manager like Bitwarden goes offline or shuts down, it could mean that you would temporarily lose access to your stored passwords and other sensitive information. This is why it's important to have a backup of your data, such as exporting your passwords to a file and storing it securely on your own device.
Additionally, many password managers, including Bitwarden, use encryption to protect your data, so even if their servers were compromised, the attacker would not be able to access your passwords in a usable form. However, it's always a good idea to regularly monitor the security of your password manager and consider switching to a different one if there are any concerns about its security or reliability.
In general, it's a good practice to use multiple layers of security, such as using a password manager in conjunction with a strong, unique password and two-factor authentication, to help ensure the protection of your sensitive information.