Relatively easy if you're single and employed. Buy a van, park it in the company parking lot. Use kitchen at work and drive to a remote area during the weekend and use solar shower, etc. Might spend $300-500 a month that way.
“Remote area” = down by the river.
Even with an incredibly spartan lifestyle, you'll have maintenance, insurance, inspection and registration fees on the van; health insurance; fuel costs (power when parked, gas when moving); phone service; gym membership (showers, bathroom); hygiene supplies/toiletries; laundry; clothing; household consumables; etc. $100/week seems like a stretch unless you're compromising on personal welfare and/or safety.
At some point you might as well just do away with the van and sleep in the office.
$6,000 per year is a long way from zero. That's ~20% of the median income.