The liquid is not processed compost, nor a special "worm juice" it's simply the water that was contained in the vegetables etc. you put in the bin.
By processing, I mean it has to be further composted, or disposed of. It CAN be used as a source of organic matter, but at that stage it could contain plenty of pathogens who could infect your plants. Composting outdoors in a traditional pile of 3 feet in height/diameter minimum sterilizes the compost by going through phases of heat where it can easily heat up to 60-70 degrees celcius.
In a worm bin the principle is a little different. In aerobic conditions (in presence of oxygen) aerobic bacteria, fungi, etc. easily dominate over their harmful anaerobic cousins. Pathogens can not grow and procreate as easily therefore are controlled. I would NOT advise putting known diseased plants in a worm compost as it does not have enough mass to go through a sterilization phase, nor should it because compost worms naturally appear after the heating phase of an outdoor compost is over, to finish the work off.
