Has a criminal ever escaped a police car chase?

Yes. It use to happen all the time when police adhered to jurisdictional limits.

All the time, even now.

Because car chases are dangerous to innocent drivers on the road, many jurisdictions have made rules to break off pursuit of the criminal if the chase would put other people at risk. Breaking off a chase is much more common in 2020 than it was 10–15 years ago, when innocent people were being killed because of the chases.

yes , O.J. Simpson

Yes, it happened out on our local interstate. Guy got away & he was free for 10 years when he did something totally stupid in NYC & got his ass caught & fingerprints matched to a cold case!!!

Happens a lot, especially in jurisdictions without helicopters.

(OJ Simpson did not get away, he was tailed by helicopters in front of national TV cameras, and surrendered at his home in Brentwood after the police let him talk to hi smother.)

Bonnie and Clyde did well for awhile, back in the day. 21 month crime spree.

A Los Angeles Times analysis found that the Los Angeles Police Department reported making arrests in 82% of chases from 2006 to 2014, well above the state average of 68%.
https://www.latimes.com/local/lanow/la-me-la-police-pursuits-evade-20180222-story.html

It happens, all the time.
That’s why you legally, have to give your identity, to a LEO.
A person, may have warrents, and need to be arrested.
Then, it’s up to the court, to decide how to proceed.

About 30 years back my husband and I evaded cops by driving onto an old dirt road that led to another county nearby on a curve. Not that we were criminals but there was this one tiny county that loved to ticket people not from their county who had military tags. My husband was probably doing just 10 miles over the speed limit but so was everyone else. The cop was driving around a curve and we were on a two-way street. He looked right at us and turned his car and put his lights on and turned around but had to wait a bit for other cars to stop to let him turn. So my husband was getting ready to pull over and I looked on the map and told him where to turn to the closest county line. Luckily we made a right just where there was a curve and we drove down to the next county. He lost sight of us on that turn. I would’ve never done it if I honestly thought my husband was speeding on purpose and if the cop was going to stop anyone else who was speeding. But either he was going to ticket us because we were not white or because he saw the military stickers and that we were from another county.

Military families and people were advised not to drive past there because the targetted the military so much and had speed traps with signs hidden in trees, but unfortunately, it would take you and extra 10 miles to drive around it and on a long drive it was hard to avoid. I was scared to death but I was more angry than scared.

For a long time, we avoided that county until we got a different car and different plates. There was even almost a ban from driving through there because the base commander was getting tons of complaints from military members and families.