The basic position is that if they are both named on the mortgage and land registry title to the property then both parties have a right of occupation which neither can deny the other. This remains the case unless there is another conflicting principal - ie. an court Injunction that one should not go near the other.
If she cannot afford to take over the mortgage on her own/pay him some money for the equity in the property and cannot agree with him that the property should otherwise be sold then realistically she is looking at making an application to Court for an order for sale. In these circumstances such orders are rarely refused by the Court.
She could see a local solicitors to get a strongly worded letter written to him explaining that she could force the sale if necessary but would prefer to avoid the unnecessary stress and expense (of both parties) by attempting to reach an amicable settlement, Hopefully this will result in his engaging constructively to resolve the situation.
If they hold their respective interests as joint tenants then she should sever this so that they hold as tenants in common and therefore their shares would pass according to their wills or under the intestacy rules (rather than passing to the other automatically upon death).
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