Since you thought that I used only one source and therefore made myself out to be an expert. Below is a list of 11 different definitions. None are exactly the same as some use the term unfaithful and some use adultery, in those cases I also have respective definitions of those term. The core is all of these definitions is "a wife with another man". Kinkly is the only one that references 'husband's participation'.
Miriam-Webster a man whose wife is unfaithful
unfaithful not faithful to marriage vows
Wikipedia A cuckold is the husband of an adulterous wife
adultery The term adultery refers to sexual acts between a married person and someone who is not that person's spouse
Collins A cuckold is a man whose wife is having an affair with another man.
affair If two people who are married, but who are not married to each other have an affair, they have a sexual relationship.
Dictionary.com the husband of an unfaithful wife.
unfaithful not sexually faithful to a spouse or lover.
Cambridge a man whose wife deceives him by having a sexual relationship with another man
Britannica a man whose wife has sex with someone else : a man's whose wife commits adultery
adultery sex between a married person and someone who is not that person's wife or husband
MacMillan if a wife cuckolds her husband, she has sex with another man
Oxford The husband of an adulteress, often regarded as an object of derision, ultimately derived from Old French cucu ‘cuckoo’, from the cuckoo's habit of laying its egg in another bird's nest.
adultress a woman who commits adultery.
the law dictionary the name given when a man’s wife has been or is unfaithful to him.
unfaithful no definition
wordreference.com the husband of an unfaithful wife.
unfaithful not sexually faithful to a spouse or lover.
kinkly Traditionally a cuckold was a married man with an adulterous wife. However, the term now describes any man in a committed relationship who enjoys his partner having sex with other people.
adultery Adultery is a term which refers to extramarital sex or sex outside of a monogamous marriage. To have sexual relations with someone other than one's own husband or wife is to commit adultery.
No accepted dictionary defines 'stag' in a sexual context. So, one may apply their own definition for their own use. For the purpose of this discussion let's use one Urban Dictionary definitions. "The male half of a relationship who allows and finds sexual gratification in allowing and even encouraging his female partner to have sex with other men." That being said the 1st test is a wife who has sex with some else. If she does the husband is a cuckold, if he participates, he is ALSO a stag. The term stag doesn't replace cuckold.
In the examples I gave a female can be called a woman and ....... It is apparent that when she is a ......, she passed the 1st test and is inherently known as a woman, the term ...... doesn't replace that of woman they coexist.
In the example of thievery, you interjected the penalty. That has ZERO bearing on the act of stealing. The act has been consummated and the person is now a thief regardless of what ensues.
For us to effectively communicate we must all work from the same basis of the meaning of words. One cannot apply their own definition. Consider: your neighbor uses his own definition of good guy as slut cocksucker. You see him out and about greet him and he shouts to you that you're a slut cocksucker.
Bottom line if your wife has sex with another person, you ARE a cuckold!