Not all die back or rot of plants growth is harmful. If the spores remain in the compost it is best to only use the compost in shrub borders not potting soil. Most compost bins do not reach the required heat to sterilise the compost.

Verticillium wilts can affect busy lizzies planted in the same soil as a previous year - and it overwinters in soil. If what killed the busy lizzies was the big problem this year, Downy Mildew, again, change the compost. But if the problem was one of the two viruses affecting them (Tomato Spotted Wilt or Necrotic Spot virus) then the compost shouldn't be affected. As it can be quite hard to tell what caused the problem, the safest thing is probably to change the compost and wash the containers before refilling.

Thank you Doctor Bob & Bamboo, these were beautifully descriptive answers to my question.