Is it permissible to marry a woman who is legally married but has been separated from her husband in intimate relations for four years, with children present, and the reason for not divorcing is to avoid cutting off government assistance?

It is not permissible to express a desire to marry a married woman, neither explicitly nor implicitly. This is one of the most egregious sins because it involves corrupting a woman against her husband. Some scholars have gone so far as to rule that the marriage of the one who corrupted her against her husband to that woman is invalid. The relationship with her must be severed, and it is not permissible to marry her until after her separation from her husband and the expiry of her iddah (definition) (waiting period). It is important to note the necessity of documenting the divorce or annulment and not concealing it to obtain government assistance.