What does a cracked digitizer mean?

I just bought an iPhone on eBay and the seller keeps saying it's fully functional with a cracked digitizer. As I recall, a cracked digitizer means the phone doesn't respond to touch, right? So, how can it be fully functional? Does this mean when I receive the phone and power it on it will be covered with those white spots? I keep asking for a picture to see where the white spots are and asking what the impact of a cracked digitizer is but he's not responding to my messages. Should I be concerned?

Why would you buy it? If you knew the touch screen won't work when you get it? In some cases you can't just replace the digitizer you have to replace both lcd and the digitizer. Not a good move.

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