The price floor for a barely-usable car in a US state that doesn't require an inspection to register it is probably around $500, but that can fluctuate as low as $0 (I literally watched a friend give a beat up, but driveable old van to a random construction worker in the apartment complex they were moving out of).

$2000 could easily get a 15 year old Honda Civic, Toyota Corolla or similar compact car with a reputation for longevity, without major issues. Shopping in that price range can, however be risky if you're not mechanically inclined enough to inspect the condition of the car and don't have the aid of someone who is.

A lot of people did recommend Honda Civics, I considered it but they also apparently are at a higher risk of getting stolen too... so I didn't get one.