Assuming that this is not stocking / wholesale finance which also shows up on HPI and is a consumer deal then I wouldn’t say it’s normal for any decent sized dealer to leave consumer finance outstanding. It’s also dangerous for the consumer as you’ve relinquished the car but remain liable for the funding.
It should come in, the HP/PCP be cleared and then go on a specialist stock funding product.
If it’s “off books” / sold as agent I don’t know where you stand on consumer rights.
Personally I’d be wary but as tallpaul says you could add a layer of protection by settling direct although some funders may balk at taking third party money for money laundering reasons. There’s also the risk that you pay and then the vehicle doesn’t get handed over.
Imo it’s better to deal with a transaction where you don’t get stuck in the middle of someone else’s finance agreements.