Is it permissible for a woman to register half of the apartment in her name, with a power of attorney from her husband, given that she contributed to its cost, in order to secure her future after being expelled from the marital home and the husband's refusal to divorce her or grant her rights?

A woman is not permitted to seek a divorce without a valid reason. However, if the husband is abusive in his marital relations, then she has the right to seek a divorce. As for using the power of attorney to write half of the apartment in the wife's name, she is allowed to do so if she paid half or more of its price and it was not a donation, and she was unable to obtain her right through legitimate means, provided that she does not take more than what is rightfully hers. This falls under the category of seizing one's right.