What is the ruling on a secret marriage for a woman whose husband has left her in limbo, refusing to divorce her, while she fears falling into temptation and he procrastinates for financial and legal reasons?

Your sister is not permitted to marry another man until her husband leaves her, either by divorce or annulment, and her iddah (waiting period) has concluded. A marriage before that is null and void, and cohabitation in it is considered zina (illicit sexual relations). Divorce occurs by the husband's verbal pronouncement, by writing with the intention of divorce, by the husband's代理人 (agent), or by a judge's ruling. The iddah begins from the date the divorce occurs or from the final ruling of the Sharia court. If your sister is harmed by her husband's abandonment, she may seek a khul‘ (divorce at the wife's instance, usually by returning the dower) from him, giving up some of her rights, and then she may marry after her iddah has expired. She must be patient and seek help from Allah until a lawful marriage becomes possible for her.