Identity theft -- your documents could be sold on the deep web. Criminals can buy them and use them to impersonate you. Most commonly, it's to steal money under your name: Opening new phone or utilities accounts, opening bank accounts and writing bad checks, opening new credit cards that will never be paid off, etc. When those accounts are defaulted on, they'll be tied to your name.

Worst case, your ID documents could be used to verify identity (for example, at a cryptocurrency exchange), and then the account gets tied to illegal activity like money laundering, theft or fraud. Many exchanges work with police in those cases.

I would avoid KYC wherever possible, and particularly with ICOs.