I have all three, Irrevocable Living Trust, an LLC, and an umbrella policy, they protect me in different ways.

The property in Manhattan was transferred from the owner to the irrevocable trust on behalf of the owner.

However, depending on their Net worth - they may be required to pay an estate tax.The wealthy use trusts for various reasons.One reason is to decrease the tax liability of the "estate tax".The wealthy are required to pay an estate tax if their net worth(or gifting during their life) is above a certain threshold at passing(5.45Million in 2016) .The wealthy do this by transferring assets to a trust and only including in their estate the value of the assets transferred to the trust at the date of transfer.Example. if your parents transferred 5.45 million dollars of assets to a trust and the value of the assets increased to 10million; they would only include the 5.45 in the estate tax calculation.You need to make sure the trust is set up as an irrevocable trust(contact a lawyer on the type of trust that needs to be set up).Another talking point is that assets in a trust are at the discretion of the trustee until the assets are transferred to the beneficiary.

She now lives in a memory care facility, and her properties are part of an irrevocable trust.

Such as an irrevocable trust some insurance wont accept those.

There are a number of reasons folks want an IRrevocable trust but if you plan financing and vesting directly to the trust, revocable is the path of least resistance.  

Family members were in an irrevocable trust and changed to an LLC partnership after the mother passed. 

If Tenant abandons the Premises or vacates the Premises upon the expiration or termination of this Lease while leaving personal property within the Premises, Tenant specifically and irrevocably waives all title and interest Tenant has to such property and grants to Agent full authority to immediately dispose of same without notice, court order ,or accountability.

Furthermore I have the following included in my agreement to purchase.V.OCCUPANCY: Exclusive irrevocable occupancy shall be delivered to Buyer, Buyers Assignees, or Buyers Agents at 5:00‭ PM on the date this agreement is signed by seller, unless a rescission period is granted to the seller according to paragraph XLIX.

Irrevocably.