What does it mean when a tax listing is a trust?

I am looking to buy a house and I looked up the tax record and it is listed as a Trust. The name on the trust happens to be the same as the listing agents last name. Does this mean the house is a foreclosure?

No. A trust is common when it comes to real estate ownership that is inherited. Thus it is more likely part of an estate rather than a foreclosure. A trust is controlled by a trustee who can sell the property at his/her discretion within the rules of the trust itself for the benefit of the beneficiary(s). Since real estate is often like any other investment sometimes assets simply get sold off to re-invest in new opportunities.

A trust just means that the home is owned under a Trust, usually by a number of family members. Not necessarily a foreclosure. Real Estate Agents may list their own property.

a trust is an arrangement whereby money or property is managed by one person (or persons, or organizations) for the benefit of another but is owned by the 'Trust'. A trust is created by a settlor, who entrusts some or all of his or her property to people of his choice (the trustees). The trustees are the legal owners of the trust property (or trust corpus), but they are obliged to hold the property for the benefit of one or more individuals or organizations (the beneficiary, a.k.a. cestui que use or cestui que trust), usually specified by the settlor. The trustees owe a fiduciary duty to the beneficiaries, who are the "beneficial" owners of the trust property.

The trust is governed by the terms of the trust document, which is usually written and in deed form. It is also governed by local law.

No, it means the title to the property is held in a trust. Quite common.