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While it's not a must, you can cut them back to about 6 inches from the ground, if desired.
I wait until spring to cut mine down, as they add some winter interest to the garden.

If they were in pots the roots may have dried out and perished.
If they were in the ground the roots may have survived. You can trim away the dead material and continue to water on a regular basis.
Time will tell.

Remember a loss in the garden makes new gardening opportunities, this reminder helps me when I lose something in the garden.

If you are referring to cutting the plants back at the end of the summer, yes, you can trim the plants back. I like to cut them down to about 4 inches from the soil surface.

Here is a link with more information.

https://www.gardeningknowhow.com/ornamental/flowers/black-eyed-susan/black-eyed-susan-flower.htm

You can leave Black Eyed Susan for the Winter garden interest and the birds to enjoy.
Go ahead and cut the flowers back now in the spring before the new growth appears.

There are a few different fungus or diseases that can be found on Rudbeckia or Black Eyed Susan's.
Thinning the plantings to allow air circulation and when watering not splashing the plants leafs can help control the spores.
Chemical treatments are specific to the type of fungus that the plants are infected with.

Here is a great article and link that will help you.

https://www.gardeningknowhow.com/ornamental/flowers/black-eyed-susan/black-eyed-susan-flower.htm
http://www.extension.umn.edu/garden/yard-garden/flowers/diseases-of-rudbeckia/

This plant will not produce many flowers during hot summer weather. It will likely start blooming when the weather cools down in the fall. Another possibility is that the soil the plant is growing in is too rich in nitrogen. Excessive nitrogen in soil causes most flowering plants to invest in leaves and stems but not in flowers.