Hey Nick! Yes, but the previous owner would have to share them with you. In their Facebook Business Manager, they can share assets like Facebook Page and Pixel and make you an admin or the owner.
If they had an ad account and audiences as well, they can do the same. Though i'd personally start with a new ad account and just share the old pixel with it to avoid billing issues.
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The easiest way to ask the current owner to assign the pixel to you. In order for them to do so, you'll need to send them your business manager ID and ask them to give you admin access. Once pixel access has been granted to your business manager, you should see it here: https://business.facebook.com/settings/pixels/
You'll then need to assign it to the person in your business manager who will be needing it (likely your media buyers!).
Last step - you'll need to connect it to the ad account that you want to run ads with by clicking on "Add Assets".