Having split up from my ex when our child was under 2 years old and I wasn't working but named on the mortgage and deeds to our joint home, I have had to do a lot of sorting out of my finances. This is my advice from my recent experience:
• report him to the police for economic/financial abuse. Speak to domestic abuse/women's charities for advice on this and see if there is any free legal advice or support to make the case to keep the property for her and the children. If this is not possible or cost prohibitive then a quick sale of the house is important.
• get on with selling the house asap. Whilst your sister is named on the mortgage and deeds she is liable for the debt to the mortgage company if he disappears and stops paying it. She also needs him to sign off the joint deeds upon sale. She is not entitled to certain financial or housing options as she has a mortgage/property so the sooner she gets shot of it the better. It opens up more options to her and maybe gets her some money from the sale. Given that her ex has been prepared to financially abuse her and shaft her like this, the fewer legal/financial ties she has to him the better.
• get her to apply for the child benefit and explain that the claimant (her ex) has moved out of the home and is not living with/providing for the children and therefore shouldn't continue to receive the child benefit (this is important as by not claiming the child benefit your sister has missed out on all those years of national insurance contributions and so will not qualify for the maximum state pension amount. She needs to be getting this sorted as a priority. It won't take long to do).
• She should apply to CMS as soon as possible. There is an option to ask them to pursue her ex for the money straight away on the grounds that she doesn't believe he will agree to pay it through mediation etc and she can tell them there have been decades of financial abuse. It will mean she loses a small percentage of the money as a fee but that's better than getting no money because he refuses her and means she doesn't need to deal with him directly.
• next apply for universal credit. This is done online and doesn't take long. She can put that there has been financial abuse and him leaving her destitute has caused a major acute depression. It will be a while before the health element is assessed so initially she may need to attend the job centre and agree to look for work. If she is still depressed by the time the health assessment happens she may be entitled to more money if they deem she is unfit for work or work related activity on account of the depression. Although it may seem daunting, contact with a job coach through the job centre/universal credit application will be helpful as she will find out about free training courses etc to support her back into work after this long a gap.
• make a GP appointment to discuss the depression so she can access support but also so there is a record of it for her universal credit claim (though she doesn't need to consent to them accessing her medical records she can ask for a sick note from the doctor to cover her claim initially until she is able to look for work/or she has been assessed by universal credit for the health element).
• if she lives in Scotland she can apply to the Scottish Government for the Scottish Child Payment. This is £100 a month per child in addition the the UK government Child Benefit. There are other benefits and help she may be eligible for. They are all explained on the Scottish Government website where you can also do the applications.
• do an application for social housing. Even though she has a home at the moment, she can still do the forms and explain there has been financial abuse and her house is going to be sold. There is probably a box to tick on the council housing online application for domestic abuse. Tick this as economic abuse comes under that umbrella. Ask the council housing department about housing association properties and mid market rents and apply for all of the above.
• alert the mortgage company, utility companies and council tax department about the situation in case he stops paying the bills. It's good to have this on record so they can advise your sister of how they can help her, should he stop paying the bills and she gets left with them. Being proactive is far easier than reacting to getting cut off etc or getting into arrears. Once her universal credit application is in the system it will help her as these agencies can talk to each other to back up what she's saying. There are crisis grants available from some councils and she can also request an advance payment from universal credit.
Once the house is sold she could effectively be homeless with 3 children in school so would be a priority for housing (if there is no/little capital from sale of house).
There may be other benefits she will be entitled to although I think the cost if living payments have finished now.
Good luck to her. It all seems a lot and very daunting but things will start to come together. Take any financial/housing help you can as a start. It's not a forever situation but these avenues of help will get her set up on her own and allow a clean break from depending on him. Then she can make her own money in due course. Just deal with the situation as it presents itself now. Best of luck to you both. Good on you for helping her out - wish I had had a sister like you.