My company had an interesting policy w.r.t. sick time.
For the first approximately 2-1/2 years of service, we accumulated sick time at the rate of 1/2 day per 2-week pay period. If one took no sick time, that came out to approximately 33 days of sick leave earned over the first 2-1/2 years.
Thereafter, the rate doubled, to 1 day per pay period. After approximately 8-1/2 more years, one hit the maximum of 246 sick days.
If or when one took sick time, it came off what one had accumulated.
But, here was the big carrot - after one had earned 246 days, there was something called a Sick-Leave Vesting Bank. You could never accumulated more than the 246 sick days, but thereafter you banked 1/4 day in the the SLVB. So, that worked out to just over 6-1/4 days per year if one took no sick time. That adds up.
If you took sick time after accumulating the 246 days, that time was taken off the 246, and had to be earned back before the vesting resumed.
I was fortunate to be pretty healthy through my career - when I retired, the company paid out close to $50K for my sick-leave vesting along with the severance package.
In the early years, there was no family leave. I did use a fair bit of vacation time for that. I saw it abused a lot, with people taking sick leave when they weren't sick.
Later on, one was allowed to take family leave, which counted against accumulated sick leave.