That depends, if the illness that they had was genetic (ie a problem with their DNA) then it wouldn’t really matter if you cloned them, they would still get the illness. However, if the disease was acquired externally say a bacteria infection then if you cloned from an uninfected cell then the clone would not be affected in the same way.
There are a few more issues to address here though. You may have heard of Dolly the sheep who was a clone. She didn’t live as long as a normal sheep because the cell that she was cloned from was old and not very good. The same would probably happen if you used one of your own cells in your body. So you wouldn’t live for a full life time.
Also at the moment no one has successfully cloned a human before and it is probably a process that would take a few attempts to get right. Also there are a lot of ethical implications about cloning some one so I very much doubt anyone would be allowed to do it.