The local authority has a right to claim back any unspent monies as it is public monies and therefore they make a responsibility that it should be spent wisely. That being said, as a Direct Payments user you are of course responsible for any costs that are associated with the costs of being an employer and this includes redundancy as set out in the Care and Support statutory Guidance paragraph 12.27.
The council should enable you to be able to do this by providing you with sufficient funds as… ‘the local authority must ensure that the direct payment is sufficient to meet these costs if it is appropriate for the adult to meet their needs by employing someone.” Paragraph 12.29 of the same guidance.
In practice, local authorities make different arrangements for providing for redundancy. Some still enable the person in your position to build up funds. Others say ‘here is a smaller personal budget, but of course IF and WHEN your staff need to be made redundant, we will be here to fund the legal obligation’. This is what you need to get from them in writing. You may be able to hold on to the money if the Direct Payment agreement you signed with the council specifies that you must save for redundancy. Alternatively they may LET you keep the money if you are managing to earn interest on it, because it would be foolish to disturb those arrangements. Any such money is held on a kind of a trust by you for the purposes intended in any event. The bottom line is that a person in your position should not be thinking of making staff redundant just because your budget is cut: you should be thinking of challenging that cut as potentially not lawful, if your needs hadn’t lessened, when the cut was proposed. See s27 of the Care Act for what MUST happen before any revision is imposed to an existing care plan!