This could get very messy. Consider this. She rents it out. Gets good tenants for years. Mortgage is paid down a fair bit. House goes up in value a fair bit. Ex-partner pops up and wants a share of the equity.
If she's still on the mortgage and looking to get a new mortgage, it might possibly work against her qualifying for a new mortgage, even if the rent is covering the mortgage payments. For the purposes of calculation, a new lender will discount the rent to allow for tax, expenses, vacant periods etc. So unless the rent is a lot over the mortgage repayment, it will be used as a liability on her income for the purpose of a new mortgage application.