If you separate and want to untangle your shared finances, you can close the account. If you have shared savings and cannot allocate them between you amicably, it is important that you let your bank know as soon as possible.
They can do things like freeze the account until the dispute has been settled. It may be useful at this point to work with a mediator. Mediators can help arrange who the money in a shared account will be given to in the event that you go to court, sometimes depending on who paid in the funds initially.