Yes-that would be what happens in most states.
The power of attorney is usually used to prevent the guardianship from happening.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.
If your "durable power of attorney" is a health care proxy (rather than a general or special power of attorney of any type) then the guardianship would supersede the POA.
Best wishes for a favorable result, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.