A man was always the offended party in adultery, since polygamy and concubinage were not forbidden. That is, if a man had more than one woman, that was not adultery, unless one of the women was another man's wife. On the other hand, a woman could not have more than one man. Thus, every woman who was not strictly faithful to her husband was an adulteress, and had violated her husband's rights. The man who slept with her had also violated her husband's rights.
As some Old Testament scholars have observed, it was not possible, under the law, to commit adultery against a wife, only against another husband. We might find this objectionable, and a double standard, but it is not a double standard about legal penalties for adultery. It is a double standard about polygamy. Adultery was still punishable by death, whether the adulterer was male or female.
The ordeal of jealousy determined whether a woman had done such a thing. If she had, there was also a guilty man somewhere. If he could be found, he was subject to death as well as she. However, if she did not expose him, he might get away with it. But this is not because the laws somehow absolved him.