A "grantor" establishes a trust on behalf of a "beneficiary" by placing property into a trust. A "trustee" is named to administer the trust and holds the property on behalf of the beneficiary. Property placed into a trust must be retitled and redeeded in the name of the trust. When you place property in an irrevocable trust, you cannot end the trust or take your property back. In contrast, you can undo a revocable trust during your lifetime. Property you place in a revocable trust can also be withdrawn from the trust.
A mortgage is an encumbrance held by the owner of property, such as a bank. This type of encumbrance is known as a lien, which is a security interest. Your use of encumbered property may be restricted. For example, you cannot sell property that is mortgaged without the mortgage holder's consent. This is because the lien prevents you from obtaining clear title to transfer the property.
You must make mortgage payments per the terms set forth in the loan agreement. A lender may foreclose if payments are not made as agreed. Foreclosure is the process of a lender taking actual possession of the property from you to pay the debt you owe. If your property is foreclosed, you lose all rights to the property. For foreclosure purposes, property in an irrevocable trust is no different from non-trust property. The only difference is that the trust is the party foreclosed upon as opposed to you individually. Thus, property in an irrevocable trust may be foreclosed.
Even if you haven't missed any payments, your mortgage may be subject to foreclosure when you redeed the property to a trust. This is possible when the mortgage includes "due on sale" language, which states that the entire balance of the mortgage is due at the time of transfer (or conveyance). Consequently, your lender may foreclose if you cannot pay off the mortgage.