It depends on where you think the parental rights may have been terminated. If in Juvenile Court , in a case you know about, if you were named as a parent you can go to the court and inspect the file, if you have identification. Normally, many notices would have been sent to the parent, and a lawyer appointed, before a parent's rights are terminated.
If the termination was in a private action, or in connection with an adoption, you may have to check the court records (in person, since these cases are confidential, they won't list on any online services, nor will the clerk's answer questions) in each place the case could be filed, which could be virtually anywhere, since often the case is filed whether the adoption parents live, or their agency is located.
If the parental rights are fully terminated, then the obligation to pay support ends. However, in some terminations for purposes of adoption, the termination is fully effective only if the adoption is granted, so the rights could seem terminated, but the child support obligation revive if the adoption is abandoned.