It depends on what kind of tenancy your sister has - if it is secure and she is the original and sole tenant, she should be able to assign her secure tenancy to you as a 'potential' successor. (As a member of her family and assuming you can prove you live at her address and have done so continuously for the last 12 months?). Look it up at s.93(1)(c) Housing Act 1985. If she can do this, she needs to do it before she leaves (and possibly before she signs for the mortgage) otherwise there is a danger the councl will argue she is not 'occupying the dwelling as her only or principal home' and has thereby lost security of tenure.
Get advice from your local CAB and maybe see a solicitor for a deed of assignment. Good luck.