How to repair burnt heat bed connector?
Owning an Anet A8 I confirm that the connectors are not rated for the amount of current that pass through them. You do not need a new bed unless the heat element has burned through (but that is pretty uncommon, it usually is the connector). This burning of the bed connectors is a very well known problem of the Anet A8 printers; these connectors are just not rated for the current and the movement of the bed. It is best not to use a connector at all! And yes, the Anet A8 default printer firmware does not have any build in protection for thermal runaway! It is always advised to immediately flash another firmware, e.g. Marlin firmware. 

The best repair is to get some high quality silicone AWG 14/16 wires and solder these directly onto the back of the pins of the connector. Also crimp forks to the other end to connect the wires correctly to the printer board.

What I did was cutting up the connector to leave only the 2 middle pins (for connecting the bed thermistor, which does not use much power) and soldered the red wire to the left 2 pins and the black to the right 2 pins. You can do that at the back side of the socket where the pins make an angle.