If my niece's uncle died and had no other living relatives, since his neighbor is the trustee can he take everything?

I cannot give you a reliable legal opinion with the information you provided, but I can give you general information.

A trustee is a person who administers a trust.  A trust is different from an estate.  If the neighbor is really a trustee of a trust (which requires a written trust agreement), then he will "administer" the assets that your niece's uncle placed in the trust.  If assets were not placed in the trust, then the trustee has no authority to do anything with them.  So, placing assets in a trust is one way to distribute them after death.

There are other ways to distribute assets after death.  The most common way is to name a beneficiary.  This is frequently done for retirement accounts and life insurance.  It can also be done for bank accounts or investment accounts.  If your niece's uncle had these kind of assets, the named beneficiaries will receive the assets without a will or trust.

The last most common way to distribute assets is through an estate.  The assets would be distributed according to the terms of the will, if there is a will.  If there is no will, the assets would be distributed according to state law.  Since this man apparently had no relatives other than his niece, she would likely inherit everything if he had no will.  An executor (if he had a will) or administrator (if he had no will) or personal representative (in some states) will administer the estate.

Whether this gentleman had a trust or has an estate, the trustee/executor/ administrator/personal representative must administer his assets according to the deceased uncle's wishes or state law.  They don't get to do whatever they want.   The only way a trustee, etc., can take anything is if they are also named as a beneficiary.

I realize this is complicated, and I hope this explanation helps.