Maybe the trust will have to file a second year, but not for this reason. An IRS refund is not income. A trust must file a tax return if it has more than $600 in income, which might or might not be the case. If the trust had no other income and is just distributing assets (the refund), no income tax return is required.
BHoffman, did you mean the DECEDENT'S primary residence and a residential rental house he owned were in the trust? If the beneficiary's own assets were in the trust mixed in with the decedent's, you have an ongoing trust and will file returns for many years. And no, if there were no nondeductible contributions to that IRA, there is no basis (all contributions were pre-tax). The whole thing is taxable. Check if the decedent has been filing 8606s to report basis.
It seems to me as if this poor guy went to one of those dinner seminars and got suckered into forming a trust he didn't need. From what you've said, he didn't have enough assets to justify protecting them in a trust (he may have had liability reasons). I have witnessed this many times--unsuspecting people fork over a fortune to form a trust they don't need, then have to pay for trust returns every year. I'm dealing with one right now where the decedent had a trust that expired on his death and all the assets were to be distributed to his son. Son called me because the jerk who set up the trust years ago insists the assets must be distributed to a new trust set up for the son before they can be distributed. Cost to set it up is $8500. I told the client to call an attorney, who reviewed the trust document, called the jerk and told him to distribute the assets directly to son. I'd report the jerk if I knew whom to report him to.