The old owner had no right to leave anything behind--once the sale closes, it is the property of the new owner. If the old owner did leave things behind, he should pay "use and occupancy" for the amount of space they take up--basically, rent. The amount is proportionate to the use those items made of space. Example: say they could fit into and take up the equivalent of one room of a 3 bedroom home. Say the home would rent, in this neighborhood, for $1,800 per month. If the items effectively took up 1/3 of the space for one week, a fair rental might be 1/3 x $1,800 x 1/4 (since one week is 1/4 of a month), or $150.00.