36,525.
A person can be drawn from age 1 day old to age 100, which is the oldest person. If a person born every single day within that span is drawn before any duplicates, then the following:
365 days per year x 100 years = 36,500
Over a 100 year span there would also be 25 leap years, and people who were born on February 29th in leap years could also be selected, adding 25 more potential days to be selected from, and therefore 25 more people that could be selected at maximum.