The symptoms suggest either Southern Blight or Verticillium Wilt, both of which can occur on Black-eyed Susan (Rudbeckia). Unfortunately, the plant will not recover, and should be removed before the pathogen potentially spreads to neighboring plants. You can try to determine which infection was the culprit by looking for the characteristic spore capsules of Southern Blight, though it's possible they would not have manifested yet, or may be hard to detect. If Southern Blight is responsible, then removing a bit of the top few inches of soil around that root ball when digging the plant out is a precautionary way to make sure spores are removed.

Miri

Thank you!  Did I do something wrong to cause this? Should I wait before planting some thing in its place? Are there certain types of plants that I should avoid?

Not necessarily, plant scan succumb to these opportunistic pathogens even if growing well. Over-watering can make root and crown rots more likely, as can over-mulching, but sometimes even good gardening practices can result in the occasional outbreak of Southern Blight or Verticillium. You don't necessarily need to wait, but choosing a Verticillium-resistant species might be prudent, and removing a bit of soil (you don't have to go very deep) can help suppress a recurrence of Southern Blight, in case it's that pathogen. Several Universities have lists of Verticillium-resistant plants  (though many focus on trees and shrubs), but we are not aware of a comparable list for Southern Blight.

Miri