I used Unsplash on one website early on, because the client was sending me horrendous images taken with her iPad and too cheap to spend a few dollars on licensed images. Not only did it take up many hours of my time for no financial gain, it also left me worried about exactly this kind of thing. I documented it all at the time and later swapped them out for images from Shutterstock after explaining the potential issues.
I had another client who endlessly persisted in sending images he had simply grabbed off Google, Flickr or other websites and that became very tiresome having to explain a dozen times in writing that stealing images from the internet is a dumb idea. That was particularly vexing because the client had pots of money and was just being silly, but in the end I managed to ensure every image was properly licensed.
Nowadays I tend to take out a monthly subscription at Shutterstock without the auto renewal enabled and based on how many images I think will be required that month for ongoing client work. At the end I bill clients for those images to ensure I make a profit and have invoices from Shutterstock with clear licence agreements. Their collection is massive so I can generally find what I need. The images are licensed under my name, so that means I can also use them on other projects if needed.
Sometimes I’ll find an image from iStock if I need something really specific, but they generally work out more expensive. There are also times when I’ll shoot something myself, since I was a full-time photographer for many years.
As a very simple rule of thumb, if a client is reluctant to spend a few dollars on images they will be a pain to deal with, so I don’t even try to appease them nowadays by suggesting options like Unsplash. Instead I insist that we use professionally produced images with a licence for web usage and explain the potential $250,000 claims on images registered with the US Copyright Office. That usually focusses their attention.