Is the wife entitled to seek divorce due to her husband abandoning her, without returning any portion of the dowry, knowing that the husband refuses to return her and refuses divorce except upon the return of the dowry, thus leaving her in a suspended state?

If the reason is not from the wife, such as insubordination (nushooz), then the husband has no right to prevent her from leaving him by paying a compensation (udhl), and this is considered an injustice. The wife has the right to request a divorce if she is harmed by her husband's abandonment of her without a legitimate reason. It is recommended to seek reconciliation and the intervention of wise individuals, as Allah Almighty says: "And if a woman fears from her husband nushuz (ill-conduct or desertion) or aversion, there is no sin upon them if they make terms of reconciliation between themselves - and reconciliation is better. And [human] souls have been made to incline to [worldly] avarice. But if you do good and fear Allah - then indeed Allah is ever, with what you do, Acquainted." If reconciliation is not achieved, then the matter must be brought before the Sharia (definition) judge to rule as he deems appropriate.