Like Bruce I l like haiku that are more than one level poems. We have a play on words about the rug:
pull the rug out (from under someone)
"to suddenly take away important support from someone"
The school pulled the rug out from under the city soccer league when they asked them to pay for using their field. CAMBRIDGE DICTIONARY DEFINITION
But also, perhaps in some yard sales etc… the part of an item where there is damage, too much wear and tear, a cigarette burn etc… is hidden under another item. The experienced yard sale visitors will know to check something better and more thoroughly.
Of course certain damage to items for sale carry their own history, whether good or bad, or ultimately a neutral history over the decades.
And also 'rug' is slang for a man's false hairpiece.
There is a lot for the reader to enjoy and interpret.
I thought the narrator's partner wanted them to get rid of the rug as it was past its sell by date (excuse the pub!) However, the narrator wanted to keep it for sentimental reasons, so they left it mostly covered up, with just enough showing that they could say if asked that it was in the sale! :)