The first case is a situation where someone lends money to a widow. The Mishna teaches that no mashkon can be taken from a widow – whether she is rich or poor – based on the pasuk (Devarim 24:17) that forbids taking a widow’s clothing as a guarantee. While some of the commentaries explain the basis for this rule based on the sympathy and sensitivity that the Torah shows towards an unfortunate woman, the Rambam suggests (based on the Gemara’s explanation) that the interaction that will be caused by the need for the lender and borrower to interact because of the mashkon will lead to rumors about these two people. If this is the underlying reason for the law, it stands to reason that the halakha will apply not only to widows, but to any single woman who acts on her own regarding business transactions.
The second case where taking a mashkon is forbidden is when the guarantee would be a millstone or some other implement or utensil that is needed for preparing food at home. The basis for this is also a clear passage in Sefer Devarim (24:6), which is understood to forbid the taking of a mill or anything similar.
The Mishna is referring to a small hand mill that was used in homes.
Hand mills were made with a hole in the top where the grain could be inserted and another on one side where a stick could be placed, allowing the grindstone to be turned. These were often used at home and turned by women who were responsible for running the kitchen. When there was a need for a large amount of flour, or when flour was produced commercially, larger mills were used, whose stones were turned by water power or by animals. Such mills could, in emergencies, be turned by people as well (see, for example, Shoftim 16:21). Nevertheless, it would be most unlikely for such difficult, manual labor to be the responsibility of the woman of the home.