If she becomes bankrupt the home will (if there is any equity in it) be taken by the Official Receiver, sold and her share of the equity will go towards paying her creditors. Your partner should then get his share of the equity. Alternatively, the OR will offer to let a third party buy out her equity interest - but if your partner is not able to afford the present mortgage payments he would presumably not be able to raise the money to do this.
So there's not much point in your partner trying to keep the moertgage up to date.
Go to the Insolvency Service website and you can download booklets on the effects of bankruptcy, including one about the home.