Some broken wands are repairable, and then can be used ‘whole’.
When Harry shows Ollivander his broken wand, Ollivander tells him that with the degree of damage his wand has, none of the ways he knows could fix it. He doesn’t say broken wands can never be fixed - if he knew that it was impossible, he’d say that rather than ‘it’s too damaged for me to fix’.
“Ollivander held out a trembling hand and Harry placed the two barely connected halves into his palm. ‘Holly and phoenix feather,’ said Ollivander in a tremulous voice. ‘Eleven inches. Nice and supple.’
‘Yes,’ said Harry. ‘Can you –?’
‘No,’ whispered Ollivander. ‘I am sorry, very sorry, but a wand that has suffered this degree of damage cannot be repaired by any means that I know of.”
- Harry Potter and the Deathly Hallows, Chapter 24 (The Wandmaker)
This indicates that, although they wouldn’t work on Harry’s wand or any wand with a comparable amount of damage, that Ollivander does know of ways to fix broken wands. This also means that there are cases where the wand isn’t quite as badly broken, and can be successfully repaired. Therefore, broken wands can sometimes be fixed into usable ones, and can have value due to that. The other things we know are in the junk shop, lopsided brass scales and old cloaks covered in potion stains, also fit the description of things that are worn-down but may be salvageable.
The junk shop seems to be a way for wizards to get used items presumably for much cheaper than buying it new and in good condition. Most wizards prefer getting new wands and would typically buy other items secondhand if they needed to save money, but pay full price for a new wand that’s chosen them. However, if they still couldn’t manage to afford a new wand, buying a broken wand and attempting to fix it (particularly because of the limited demand for secondhand wands) would likely be a lot cheaper than the seven Galleons needed to buy a new wand from Ollivander.
“Most witches and wizards prefer a wand that has “chosen” them to any kind of secondhand wand, precisely because the latter is likely to have learned habits from its previous owner that might not be compatible with the new user’s style of magic.”
- The Tales of Beedle the Bard
So, it’s possible they sell broken wands for wizards who can’t afford new wands to mend and use.