Widows carrying on a trade after their husband's death was indeed pretty common and perfectly legal- a widow had control of her property, and so was more free than she had been as a daughter or a wife. Although women were expected to run the home, the home was also in the business: apprentices were, by contract, fed and housed, and it is reasonable to suppose that a housewife of a prosperous tradesman would be already therefore doing a good bit of managing, might also be handling a lot of the business bookkeeping- especially if her husband often had to be away on business. David S. Landes even thought he saw a common pattern in the 18th c. watchmakers of Switzerland and the Jura , where the master of the shop would die, the younger head journeyman would marry his widow, then the widow would die and the journeyman would re-marry to a younger woman who would then outlive him, marry the head journeyman, etc.

There were also women in their own businesses, carrying on trades. There were not too many trades that would take women as apprentices, however. It was a time in which most people were worked very hard, sometimes worn out by early middle age, and apprentices were a part of that. A carpenter would be much more likely to take on as an apprentice a big teenage boy rather than a teenage girl simply for the greater muscle mass. It may seem sexist to us ( and sexism was definitely a part) but it was also just grim economics. Women apprenticed more often to do things like dressmaking, embroidery, millinery (hats), hairdressing. But there were a few specialties where women were thought to be better because of having more dexterity (I think forging fine chain was one- but I can't put my hand on the reference for that). And there were examples of women just learning how to do a craft- Anna Maria Hoyland advertised in the Boston area in 1757 that she did any kind of tin or "braziery" work ( like soldering a patch onto a copper kettle) just like her mother did.