Many of the common class wore home-
knitted stockings. Two things were used to keep those socks from falling.
Another way to keep a sock up was ribbing. The rib stick was used to keep the sock tight around the leg, especially for a working man's socks.
Not all socks were homemade. From the late sixteenth century onward, knitting machines were used to make socks. These too would have had the ribbing stitch included.
All of this changed in the 1930s. Nylon was invented, allowing for the creation of elastic. Garters went out of fashion after that, for the most part. Wool as one the main sources used to make socks also went out of fashion after this.