If the company is no longer in business, you may have a chance. However, in my experience the reason SMBs want to remove Yelp listings is because they have bad reviews.
Even if you were to get a listing removed from Yelp, it may take a while for that URL to drop out of the Google Index. And then, any user could add the listing back in by leaving another review for the business.
If it’s a review problem, the reviews are what need to be “fixed”.