There are several reasons that the one parent died:

1. It could have been attacked by a predator which accessed the birds on the ice by walking onto the ice.

2. It could have hurt its leg by slipping from the ice, falling below and had a hard time trying to get back onto the ice.

3. It could have slipped and strained its leg or caught the leg on the ice and was severely injured. If so, by flailing, the injury could have worsened and the bird either died from the leg injury or from freezing.

The reasons that the other swans may not be leaving probably are not related to the other swan's death. More than likely:

1. The young swan cannot fly as it may not have its flight feathers yet and the parent does not want to leave it.

2. The weather is so inclement that they cannot fly out.

3. The ice is so slick that the swans cannot get enough traction to fly off the pond.

If there is an area on the pond that still has water, the swans can survive by at least having water to drink and possibly accessing some food even if there is very little to be found. The Regal Swan