I am in the process of appealing a living together decision (if they would ever formally give us the decision, but that's another matter) which I am pretty confident will be overturned at appeal, but my question what should my client claim in the meantime?

Background: client used part of her late husband's estate to help husband's friend with the deposit on a new house, with the understanding that her son would own x% of the house when it was sold. Her health worsened and he lost his job so she moved in to the house, he made a claim for JSA and MIR and she carried on her claim for IS and also claimed MIR. She has received basic IS with DP but no SDP (and DLA MRC) and he has received JSA up to when the compliance visit was done. They now have both had benefits stopped.

We are requesting that the DWP pay IS and JSA pending the outcome of the appeal, but don't know how likely that is. Should thay put in a claim as a couple? Would that not mean that the waiting period for MIR starts again? And will it prejudice their appeals? Any ideas of what to do in the mean time to stop the bank repossessing the house?

LT is not an exclusion reason for income support or JSA. If an LT decision has been made then both parties should have been notified and advised that one must claim for the other. If no reply is received to this then the DWP can decide who is to be the claimant -as both parties were claiming, the DWP is already aware of all their financial circumstances so do not need another claim form. In the circumstances you describe, if the house owner claims it will not affect the waiting period for MIR as this is a change of circs and not a new claim.
Are you sure an appealable decision has actually been made yet? Both their benefits may have been suspended pending a decision on who is to claim for the couple.

My client hasn't received a decision yet but her friend has - this is the only reason that we know that there has been a decision made.

So, if they don't claim as a couple whilst they're appealing is it right that the DWP will decide who is claiming for them both, so they'll get paid and they'll get the MIR as they've already served the waiting period? (They don't want to claim as a couple as they're not a couple, and there are lots of issues to do with him being a friend of her late husband.)