Legal Question in Wills and Trusts in California

A trustee has the duty to preserve and maintain the value of the assets of a trust, and that may include notice to raise the rent of an asset to preserve the asset value and the asset value of the trust as a whole.

That would depend on the terms of the trust, the number of beneficiaries, and their respective rights under the trust.

Unless the trust document specifies that the beneficiary in question can live in the property without paying rent, or there are other extenuating circumstances, the answer is "yes." This is part of the trustee's duties to maintain the value of the estate.