If the trust is a revocable grantor trust (i.e.: the grantor is the trustee and the beneficiary and can change the trust any time), then it is invisible to the IRS and is indistinguishable from the grantor. While legally the ownership changes, for tax purposes the trust is disregarded.
If the trust is irrevocable (i.e.: the grantor has no control over trust document once it is created), then the trust is its own legal and tax entity, and the grantor has gifted the property to the trust. The grantor needs to deal with the gift tax, the trust needs to file informational return and pay tax if income is not distributed to beneficiaries, and the beneficiaries will pay tax on the income distributed. The tax basis for the gifted property remains the same as it was for the original grantor.
Since it's a foreign trust, there are additional complications since the legal determination of the trust is by the local jurisdiction. What may be irrevocable in the US may be revocable there, and vice versa. What may be a trust in the US may actually be considered a corporation there, and vice versa.
Bottom line: if this scheme has any effects on taxes - it would be for the worse. If the intention is to try and save on taxes - then you won't.