The six month good cause backdating period cannot be extended at all, but as this does not sound like her first claim there mioght be a possibioity of revising one or more earlier decisions to end previous awards.
For example, if, say, nine months ago the claimant’s IS ended and the Council’s Benefits section ended HB because they couldn’t establish what the claimant was up to, they can still entertain an application for revision of that decision (which you can make on the claimant’s behalf) – if it is clear that she has not had any money during these periods the Benefits section will, I am sure, look very sympathetically at any application to revise. This can be done up to 13 months after the decision was made.
In addition, there is a loophole in the rules governing time limit for bringing an appeal to the Tribunal. A statement of reasons can be requested at any time, and this has the effect of refreshing the right to appeal for another 14 days. If the claimant then does appeal (and she must personally sign the appeal) the way is opened for the Council to revise its decision locally without the need for a hearing.
In summary, if the claimant’s circumstances are fully explained to the HB section and if they are satisfied that there is a technical “opening” that will allow them to revisit any decisions they have already made, I am sure they will be more than happy to do that.