Having worked in council tax the charges came in because less revenue was being collected from empty houses (50%) than a single person living in it (75%)
An "A" class exemption was for unoccupied and uninhabitable but that was for a 12 month period. Then it went into the 50% charge. A "C" charge was empty and unfurnished usually between tenants and was for up to 6 months.
Councils were given authority to charge what they wanted for empty properties and could charge up to 90% but this would lead to people lying and saying 1 person lived there to get the charge down to 75% so the council I worked for went with 75%.
This may all seem money grabbing but consider the local amenities the money supports you may reconsider your view, especially places where there are lots of second homes for people who visit at the weekend to come to the seaside.
I think it is poor of the council to back bill 6 years but unfortunately the computer system doesn't allow you to fudge stuff through. There has to be a charge raised but I think it is appalling that it took them this long so sort it out.
Your friend can sell the property for peanuts or pay someone to make it habitable or do it herself. The issue here is your friend is seeing £££ signs where she realises the potential of what the property could fetch rather than what it is worth now. Hard decisions. Owning a property comes with responsibilities.
And yes, the A class exemption meant people ripped out kitchens and bathrooms to make it fit the uninhabitable charge when they lived in another property so that wasn't their sole and main.