Every place I worked had things differently.
Some were per year. Jan 1 you got 10 days of vacation and 10 days of sick leave. Neither accrued, if you didn't use them, they went away. Under these circumstances, it actually seems to encourage "mental health" days. Other places I worked, you accrued leave as you worked, so for every 40 hours worked, you got maybe one vacation day, and half a sick day. I can't really remember the numbers. Most of the places with that system have an amount you can carry over, up to a certain number of hours. One of the places, accrued sick time counted towards more pay and benefits at retirement. Accrued sick time could also be donated to someone in need. This particular feature is really nice for people with serious illness. My BIL worked for the State of Alaska, and all his cancer sick days came from accrued and donated leave.
In the last two places my dh has worked, there is no real policy for sick time. You take it if you need it, and unless it is excessive, no one much cares. I think the managers probably have to keep track of the amount of sick leave taken by the department, but it mostly seems to be a honor system. I think this has worked well for those companies.
One of the best systems I've seen, from a now defunct company, was a "personal" account. This account had a set amount of money for each employee, and it did go up with salary and responsibilities. From this account, you bought health insurance, life insurance, disability insurance, vacation and sick days. It had the rewards for not squandering sick time built into it. The less sick time you took, the more money you had for vacation and other things. They may have included a basic employee-only insurance, and any additional could be purchased out of the fund, but I don't really remember.
Every place I've worked, if you used up your sick time, you were out of luck until you accrued more. Most places would let you take one extra day over accumulated leave. When I got very sick and missed almost 6 weeks of work, I had to take it as time without pay. I'm just grateful that they held my job for me.