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You are not liable for his loan whatsoever (unless you signed something as a guarantor or co-signor). However, the lien would still be on the property meaning that the bank could foreclose if the loan wasn't paid. You would lose your interest in the property if this were to happen, but the foreclosure would not affect your credit.
It is not on your credit because it is not your debt. If your dad personally signed for the loan it would be on his credit. If your brother were to default on the loan, it would not show up on your credit (and maybe not even his if he did not sign for it).
In foreclosure proceedings, the lender must notify the owners and/or occupiers of the home. The owner of the house (from what I have gathered from your question) is the trust. This means they would notify the trustee of the trust. The trustee should notify the beneficiaries of the trust if and when any trust asset may be foreclosed upon.
Having the note would allow you to collect the loan amount if he were to stop paying the loan and you had to buy out the loan to save the property (i.e. you would have more of a chance of being repaid). However, if your brother were to stop paying the loan to the bank (who also has a note) there is no guaranty that he would pay you either. But just to reiterate, you are not responsible for the loan, but can pay it off to save your interest in the property.