Whether or not the beneficiary can deduct the expenses depends on what type of trust it is and whether the beneficiary is also the grantor.
Is the beneficiary also the grantor?
Is the beneficiary related to the grantor?
Is it a revocable or irrevocable trust?
Does the beneficiary, as the grantor, declare all of the income of the trust on their own 1040 ( aka grantor trust) ?
Thank you for the information to give a proper answer to your question.
The Internal Revenue Code defines a grantor trust as a trust in which the grantor has one or more of the powers specifically described in Internal Revenue Code Sections 673 to 677.
Income earned by a grantor trust is taxable to the grantor, not the beneficiary. To the extent that a trust is a grantor trust all of the income, deductions, and credits flow through to the grantor and are included on the grantor's own personal tax return.
From the article at http://www.aicpa.org/pubs/taxadv/online/jan2005/savoth.htm
Trust distributions to a disabled beneficiary may result in taxable income. The beneficiary will report as income his or her share of the income distribution deduction calculated by the trust. If the trust makes a distribution by paying the beneficiary's personal expenses, the expenses are not deductible by the beneficiary, unless they qualify as a reduction of adjusted gross income or as an itemized deduction. Qualified payments can include deductible medical expenses, such as the costs of prosthetic devices, adapting a car or van for a handicapped person, prescribed drugs, nursing services, a wheelchair or a hearing aid. The trust is entitled to an income distribution deduction for the payment of such personal expenses; however, it cannot deduct the payments of the beneficiary's medical expenses.
So, generally it is possible for a beneficiary and not the trust to deduct medical expenses paid for the beneficiary for trusts such as the one you describe.
Please be aware that trust funds provided by a third party may disallow a deduction for medical expenses. See Rev. Rul. 77-230
"To the extent medical expenses arising from or related to the injury are compensated for by the United States and not by the individual, the individual is not entitled to a medical expense deduction for such expenses under section 213 of the Code."
Of course, you should confirm that the trust documents and the payments conform to the requirements mentioned in the above references in your case.