Can I Go To Jail For Getting Evicted And Not Paying Past Owed Rent?

No
Not unless you are still on the premises after the court date that you should have been out of the property. Then, you can get arrested for trespassing or squatting.

What will happen possibly, is the landlord can take you to small claims to get a judgment for the back rent you owe, plus any damages to the property.

I would say no, For not paying rent alone. You would not go to jail just for that, but, if you lied on your lease application and said that you made more money than you actually do, that would be fraud. Then, You could go to jail for that.