I think we probably need to be clear here on what the 'exemption from tax' is that we are talking about - as there are a lot of them!
The proposal under consideration, if I have it right, is for the OP's parents (the settlors) to establish a will trust whereby a discretionary trust (DT) would be established on the last of their deaths for the OP (beneficiary) into which assets are 'settled'.
The taxes that are potentially involved here are:
1. Stamp duty,
2. Discretionary Trust Tax (DTT),
3. Income tax on income earned by the trust and capital gains tax (CGT) on trust gains,
4. Surcharge on undistributed income, and
5. Capital acquisitions tax (CAT) on distributions out of the trust.
1. No stamp duty charge arises on the transfer of assets into the trust (on death) or on appointments of assets from the trust to the beneficiary.
2. The charge to DTT kicks in if the settlor is dead and the there are no beneficiaries under the age of 21. It looks like that will be the case here. Revenue recognise that there may be a genuine need to provide a DT as a measure of a financial protection for a vulnerable beneficiary such as an incapacitated adult and there is an exemption from DTT where a trust is for this purpose. It would have to be verified if the OP meets this hurdle. This is not an automatic exemption - it is necessary to make an application to Revenue when the trust is established providing them with a medical certificate from a doctor confirming the beneficiary meets the conditions for the relief to apply. Exemption has to be claimed on Form IT4 and agreed by Revenue.
https://www.revenue.ie/en/tax-professionals/tdm/capital-acquisitions-tax/cat-part05.pdf
3. A protective trust (like what is being proposed here) is subject to income tax (and CGT too, though I'd have to double check this).
4. Any income not distributed out of the trust is subject to a surcharge even if it is a protective trust.
5. Assets distributed from the trust are in scope for CAT. If the total amount distributed is less than the Group A threshold of €335,000, then there is no CAT. Also, if you are permanently incapacitated because of physical or mental infirmity, distributions exclusively for the purposes of discharging 'qualifying' expenses are exempt from CAT. Qualifying expenses are expenses for medical care, including the cost of maintenance associated with medical care.
It is difficult at this remove to advise as the level of assets, the extent of your incapacity and what you intend to do on the death of your parents is unclear. For instance, the plan is to inherit the one-bed property that is ear-marked for you and a share of the family home which will most likely be sold. What is the status of the one-bed property now? Is it rented out? When you inherit the property on death will you come off HAP and move in to the property? Your principal residence is outside the scope of means testing if I understand correctly. How much extra do you intend to inherit from the sale of the family home?