looking for advice on behalf of mum and her partner

ok so long story short my mum is on E.S.A . her partner is extremely unwell and going through all sorts of tests however is still on j.s.a as he has not got a diagnosis yet! they had a mortgage on their house . paid interest only .they were forced to sell house as mortgage time up. they made various improvements to house i.e new kitchen bathroom which personally cost over 10k whilst they had the house .they have been told they will receive around 16k after all fees taxes have been paid for sale of house . they are not pensioners yet mum is 64 years old and partner is 63 . they are homeless at the moment although they are staying with family . she has been notified by esa that she will lose her entitlement to benefit??? her partner will lose entitlement to j.s.a and been told by esa she cannot gift money to her kids / grand kids as this is disposing money for benefit purposes or something like it .they have no other savings or money in isa etc and no provision for funeral expenses and didnt have the money spare whilst working to set aside money for pension old age . so in a nutshell they paid a mortgage for 15 years and improved the house and the only people that will benefit from it is the mortgage company estate agent and the government is this right. please can you clarify any steps they can take to retain their benefits . mum is entitled to e.s.a as she is disabled .be great if they can retain at least some of the money for retirement thanks in advance for your help