Intentionally cancelling a credit card with a negative mileage balance is akin to cancelling a credit card oweing them money and refusing to pay. I think that some credit cards may ask reimburesement for the negative mile balance. Not recommended, IMO.

Smetimes mileage credit cards offer miles for balance transfer. If this offer is made without cash advance charges, it is often worthwhile to get the miles (try to minimize any APR charges that you would incur in this case).