(edit - i live in the us) i can purchase extra insurance for short-term and for long-term sick leave.
right now, i have ten days of paid time off for whatever reason per year (no explicit sick leave) and i pay about $650 a month for insurance which covers very little for myself and my kids until i have spent at least $6000 on any one of us or $15000 for all of us together. i make about $50k a year before tax and insurance.
and our compensation package (paid time off and insurance) is considered pretty good for my area.
i could buy better insurance and short and long term leave, but this would cost about half of what i make. unfortunately, half of what i make already goes to rent.