I can think of some:
1. The super popular option is living with your parents — either free or with below market rent. LOTS of Singaporeans do that.
2. Some people live on boats. It's possible the total cost of housing is lower that way. (Can also be higher of course. Just get a huge luxury yacht.) I read an interesting blog article written by someone who's doing this partly for budgetary reasons.
3. Employer-provided/worksite-based housing such as religious housing (resident monks, priests, nuns, etc.), classic "bed above the shophouse" arrangements, live-in tutors/proctors/educators supposedly keeping an eye on residential students, domestic worker arrangements (such as home caregivers, live-in chauffeurs, live-in chefs, etc.), dormitory dwellers, cruise ship staff, certain hotel staff (such as the head chef who probably gets a nice room), Singapore's diplomatic corps (albeit not in Singapore but on Singapore national property overseas), and the very special resident of The Istana. I know of a boarding school teacher who has taught at 3 schools so far who gets his housing (and for his family too) from the school.
The employer-provided/worksite-based housing might be "paid for" via a lower salary/lower wages than otherwise, but it's probable the total adjusted housing cost is often much lower than it would be for a comparable HDB flat.
4. Changi Prison.
5. Residential services at the Institute of Mental Health (and any other such institutions housing serious cases).