Is it legal to borrow money after discharge while case is open in chapter 7 bankruptcy?

From when a bankruptcy case opens until the case is closed or the trustee abandons property, the property is controlled by the trustee. If the value increases, the trustee can sell the property at the increased value and use the proceeds of that sale to pay the his fees and the creditors. Trustees are ALWAYS open to negotiating a cash payment rather than the sale of property. Property sales are expensive - realtor commissions, appraisals, closing costs - and uncertain - sometimes there are no buyers when a property is put on sale. By negotiating a settlement for cash instead of selling the property, the trustee avoids all these problems.

First things first: it's almost always worth it to hire a skilled bankruptcy lawyer to help you. There is appellate authority that the increase in value of an asset which the debtor has exempted belongs to the debtor. Arguably, the Supreme Court of the United States raised a question about that doctrine some time back, and you need to check what the rule is in your federal circuit and district. It sounds like the Trustee held the case open precisely to market that asset. If you offer him money more or less equivalent to what he would net from the sale of the house (after costs of sale and your exemption), then there is a reasonable chance that he will decide to take the money instead of trying to market the house. Find a good lawyer to state and argue your case.