Why? They aren't dangerous, like drugs or guns or alcohol or tobacco. They will probably be auctioned off, as if they were the proceeds of crime, eg like when a drug-dealer's car gets seized.

Yes. There are three main ways to get rid of unwanted coins:

• Send them in a transaction that has a spending script that always returns false. Technically, consists only of OP_RETURN. This is provable and does exactly what you want.
• Send them in a transaction with zero outputs. This doesn't destroy them, but it distributes them in a more or less random way, to the miner who mines that block. It's better - less deflationary - for the community. We would want to be sure they weren't broadcast in a way that favoured a miner who was connected to the public servant charged with getting rid of them.
• Send them to a nonsense address for which it is unlikely that anyone knows the private key. This isn't quite provable, although if they use an address like 1crimedoesntpaycrimedoesntpayguys and it turns out someone has the private key, they probably deserve the money.