A tied cottage is a dwelling house typically owned by an employer that is only rented out to their employees, If the resident leave their job for any reason then they must move out of the house. Thus the employee is tied to that employer. This was a common practice in nineteen and twentieth century rural England, where the landowner, that is aristocracy or a farmer, had total say on who lived in these houses. There were tied cottages on the Sandringham estate.
It was justified by the landowner saying that there were a limited number of houses in the area and he couldn't manage the estate unless he provided the house for a worker.
This was easily abused by the landowner, who use the threat of eviction to prevent workers leaving his employ, or sack and evict workers who were not of his political persuasion, for instance during the Burston school strike. Thomas Hardy uses this as a plot feature in his novel Tess of the d'Urbervilles.