Legal Question in Family Law in Texas

It's impossible to answer based on the limited info presented.

Texas has no legal separation.

But the question is a landlord/tenant question - not a marriage question.

If your name is on the lease, then you are liable for the lease. If the lease is broken, then the company will sue you. You signed a contract and you are liable for the contract if the landlord wants to hold you to it. Just because you moved out does not void the lease. The lease is between you and your landlord - not you and your spouse. So contact the landlord. Read your lease. The written contract that you signed is the document that controls - what the written contract says is what the judge will make you follow.

I hope this information is helpful.