If you leave state lines and the landlord decides to sue, he can have you "served" (notified that you are being sued) with an order to appear in his state. If you don't appear, the landlord will get a "default judgment" - meaning he automatically wins his case.
If it is a small claims case ($3,000 to $5,000 claim - depending on the jurisdiction) and you don't show up, the court generally will not issue a bench warrant for your arrest, but will simply enter the default judgment against you.
Next, you'll be ordered to pay the judgment in full within 21 to 30 days (again, depending on the laws of his jurisdiction). If you don't pay within this timeframe, the landlord can move to the collections phase of the judgment. He may decide to hire a collections agency to go after you - which may end up garnishing your wages, seizing money in your bank accounts, intercepting state tax returns, or other collection remedies as permitted by law.
Wage garnishment - varies by state. Some states (such as Texas) prohibit garnishing wages alltogether. Most jurisdictions allow the garnishment of wages of up to 25 percent of your income.
The smartest thing to do would be to get in touch with your old landlord and make payment arrangements. If you don't, your credit will eventually get ruined and your life will be made a living Hell.
In most cases, the plaintiff has seven years to collect the debt, and your credit will be ruined the whole time. So unless you don't plan on buying a car, renting an apartment, taking out a loan, opening a new credit card, or applying for any job or anything that requires a credit check for the next 7 years, this will haunt you for years to come if you don't take care of it.
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I'm a debt collector