You should be able to find adequate answers to your question here on the IL DMV website.
In most states, you are suppose to surrender or exchange your license for an in-state one once you have declared residency. In most cases, the state will keep the old one. I am not sure if they tried to do this that they will not be required to re-test under IL standards. You will have to check and see.
That said, it does not necessarily mean that they have increased their exposure by simply driving with their FL license and so long as it is valid they are legal drivers. I would be concerned however that the insurance company may pull coverage if they have not been forthcoming regards to their state of residency and current license status.
You may want to ask your ins provider as well.
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If your parents are fearful they will not pass the driving test, then they should not be driving and you should not be enabling them. Hopefully you are working with your parents to establish alternate means of transportation for them. Their estate attorney should not be advising them about their ability to drive safely.