These are the home made dust covers that drop casually over furniture, or squares to cover beds for protection when not in use.
Housekeepers covers are not exactly fitted – they are quickly made and more casual than the loose covers or slip covers that are chosen as alternatives to fixed upholstery.
The origins of housekeepers covers is simply that when upholstered came into being it was the height of luxury, the fabric was highly expensive and needed protection from sunlight and, in fact, use. In the homes of those who could afford such grandeur, families moved around between summer and winter and the simple white housekeepers covers were a cost effective way to protect the upholstery that was not in use from dust. The family crest or initials were very often embroidered at the centre back
Housekeepers covers are sometimes kept in place all year, removed only for visitors, but for the most part are used seasonally and sometimes to create a change of scene, to lighten the surroundings for the new season.
When we choose to make less well fitted covers, other than dust covers, for stylist or practical reason, we refer to them as housekeepers covers just to denote that they won’t necessarily hug the upholstery beneath.
That’s not the same as carelessness or poor cutting….