If one member of a couple is not able to make a new claim, eg. due to being very unwell, their partner could make the claim for both of them.
Reg 9(5) of the UC etc Claims and Payments Regulations 2013 states:
Where the Secretary of State considers that one member of a couple is unable to make a joint claim with the other member of that couple, the other member of the couple may make a claim jointly for both of them.
Getting this rule implemented for an offline (telephone) claim might be tricky in practice. If they are told by the Helpline that it is not possible, they could try calling again to speak to someone else! Quoting the above regulation might help!
Another option that might be appropriate, if the partner is not able to manage their affairs, could be for the partner to apply to be their appointee, and make the claim on their behalf that way.