Legal Question in Wills and Trusts in California

No--they can sign a trust and move assets into the trust, if the power of attorney document authorizes it specifically. If the principal (person for whose benefit the power of attorney document is) cannot express their wishes, any estate planning done using the power of attorney shouldn't change previous beneficiaries (or intestate succession if no prior estate planning or beneficiaries), as such a change could be easily contested.

A substituted judgment petition can be brought in court to make a will or trust (or both) for incapacitated persons as well.