I might be talking rubbish here, but I have a memory of seeing this discussed in a documentary.
It was something along the lines of, because married women were not legal entities, their husband's were responsible for any debts that they might rack up, which obviously could lead to them being imprisoned for debt if it was severe enough.
It was relatively easy to get into debt because most businesses that supplied goods to people, such as butchers, bakers, dressmakers etc were expected to work on a system of credit. So you would order your goods, receive your goods but pay for them later. So in theory, women could rack up a lot of debt in their husband's names. These notices were an attempt to prevent them from doing that.
I don't think it always necessarily means that the couple were separated, although it will have done in some cases.
