You can be named as the executor or the trustee under someone's document and not be notified of that fact.
However, once the person dies or becomes incapacitated you can always decline to act. You cannot be forced to be an executor or to be a trustee. It is completely up to you, you must voluntarily accept that position.
If you decline to act, the documents will either name someone else to step into your shoes or the beneficiaries petition the court and request to have someone appointed.