Adult sister with autism - How do i help?

Hello, My older sister is 36 years old. She was diagnosed with Asperger's when she was 28/29, so quite late in life and I feel that she has been neglected by the system  She has huge social anxieties and has never been able to hold down a job, the biggest struggle is getting a job in the first place as interviews are her worst nightmare. She has always lived at home with my mum but is very isolated, she has one friend who also has autism however he is a lot more outgoing than her and so holds down a job and has lots of friends and a girlfriend, all these things I cannot see my sister being able to do. My mum is 70 this year and still works in order to support herself and my sister. I worry what will happen to my sister when my mum dies one day as she seems unable to care for herself. She doesn't cook, pay bills, have a lot of skills that a 36 year old should. In addition this has effected my mum's life massively as has devoted her life to my sister who when frustrated can lash out and be violent which is another concern of mine. 

She was recently turned down for Universal Credit as they deemed her able to work, yet they really do not seem to understand the crippling magnitude of her condition. She worries and has cried over this relentlessly. In addition she has been on anti depressants since she was about 18 and about 10 years ago had a severe bout of depression where her weight plummeted to 5.5stone as she gave up eating (she didn't have an eating disorder she just gave up caring) they helped her and put her on new medication which has helped but made her gain a huge amount of weight so now she is overweight and very unhealthy. 

She rarely goes out without me or my mum and even then it's to the cinema or to the shops. My main concern is what will happen to her when my mum goes as I am 32, do not live locally and have my own family to consider and care for.

This has been a constant worry for our family over the years and we just feel there is no help out there. Seems to be lots of help and programs for autistic children that i hear about but autistic adults seem left to flounder. Any advice would be welcome as she is my sister and i love her but i cannot take my mum's place when she goes.