A court appointed fiduciary generally "stands in the shoes" of the ward; his or her powers are usually the same as those previously held by the person who is now under a disability. So, if the person under the disability could have closed the account, now the fiduciary can close the account.
That power can be significantly affected by the specifics of the law of your state; e.g. the fiduciary may need the permission of the court in order to close the account. (Ask your bank's legal counsel what is required.) If so, the court will want to know where the money in the account came from; i.e. the ward or the joint owner, and whether the survivorship provisions reflected part of a plan on the part of the ward to transfer his or her property at death.
A resource you might want to make available to all court appointed fiduciaries is CFPB's publication: Managing Someone Else's Money: Help for court-appointed guardians of property and conservators. Note that it is not specific to the law of a particular state.