My question involves collection proceedings in the State of: California

Hi! I've been to the California for about 2.5 years, I am not a citizen, was here on an L1 working visa. I got a job offer outside of the US, and I am keen on taking it.
However, as I am renting an apartment, the penalty for early termination is around 6000 USD, almost 2 months of rent - which I really don't fancy paying. It's kind of enforced, no one is giving any apartment around San Francisco with better terms. Anyway, I am considering telling the management good bye. As soon as I move out, they can rent my space for around 15% more than I am paying now, basically in 1-2 weeks as there is a huge shortage of housing in the Bay Area.

Question:
Are they likely to go after their early termination penalty?
Can they do anything to me as soon as I left the US? I plan to keep my checking account open with way more than 6000 on it.
If they file anything against me - would it affect me if I need to visit to US in the future? I might need to make short business trips. I would be really unlikely to move back, so do not mind a ruined credit history, but it would be awkward if I had problems on the border.
I do not want to leave any other debt, car, credit cards, phone, everything will be paid off, not abandoning them, what's fair is fair. - just this one is something I dispute.

I would appreciate if I would not get lectures on how I signed that lease agreement and I have the legal and moral obligation to pay. I am aware of this. Though show me a lease agreement which allows moving out other then the tenancy end date, and how should I arrange my life around it. So I would heavily dispute the fairness of this Early Termination Fee.

Thank you,
Peter