
I recently finished working at a rehab, and used to deal with all benefits for clients, housing and sickness benefits. Unfortunately the system is deeply flawed, for example people who can't cope with work due to anxiety/depression are having their benefits cut left right and centre, mainly because they can hear, speak and have fully functional limbs, the new assessments and medicals don't take into account properly the other ways people may suffer. And as others have mentioned they are very disorganised, often don't call back when they say they will etc etc.
You should be able to manage all calls if you get them to put it on the system and you know the security questions. Have you tried going into the jobcentre and getting an advisor appointment? Sometimes that can help get you in the right direction even though your relative may not be looking for work. I was lucky enough to have a good contact at the local job centre which enabled me to argue most peoples cases through, as often I knew the specifics of the system better than the people doing the job did!
Also, just keep working at it, be persistent and unfortunately you have to be patient!