If you commit a crime, moving out of town isn't going to help you avoid the police. If you're wanted, you can't safely drive, or have a credit card, or a bank account, or have a home with utilities, or have a job with a reputable employer. That's a hard list of things to give up.
It's not conventional, but people do make all of those purchases with cash.
Any new car is going to be over 10k, which means you need to either report the transaction or get a loan from a bank... who is going to want proof you can pay it off.
Housing is the same thing. So yes, you can use cash- but you're going to have a hell of a time using cash that doesn't have an obvious, legal source.
from: http://www.fincen.gov/statutes_regs/bsa/
These wouldn't prevent you from making a purchase, and you might falsify information sufficiently to avoid association with your real identity and drawing unwanted attention, but it's another hurdle.