I work in the United States.
The employee handbook should address this, it should also tell you when all your benefits stop.
In all companies where I have worked there has been a written policy that addresses vacation or PTO when an employee leaves.
They have all fallen under two options:
- They pay you for your hours at your normal hourly rate in a lump sum after your last paycheck.
- They pay you in a series of 'paychecks' each of which has 80 hours of pay for for vacation/PTO.
When sick was a separate bucket they didn't pay those hours, but under the PTO plan there is no way to separate the hours. The policy should also address floating holidays and other similar plans.
In all cases once you stopped coming to the office, you were no longer an employee and were free to start work for your new company.
Note: in one case employees were given an option regarding the payout of PTO. Lump or two weeks at a time. The difference is that a bigger check has an larger initial chunk taken out for taxes, but you get it all at once. At the end of the tax year it makes no difference which method is used, but it could make a difference to some people in the short term.