In Texas, can an apartment be leased to a new occupant before the original occupant moves out?

I've been going month to month at my apartment, and it has been costing $150 more than my regular rent used to cost. I turned in an intent to vacate 60 days prior to my lease expiring. About a week later I found out the house I was buying was in a flood plane, so I backed out. I went to the leasing office and said I wasn't going to be moving after all, and wanted to go month to month. I'm half way into my third month and the leasing office called saying I need to turn in my keys because my apartment has been rented? Is this legal? Is this possible?

You should check with an attorney in your state for a specific answer. I can say generally this: If you sign a lease, then you have acquired a leasehold interest in that property that (barring a breach) will not expire until the end of the lease. Your problem is that you do not have a lease. You have what is called a Periodic Tenancy. The *general* rule is that you are entitled only to notice equal to one rental period (in your case, one month). That being said, this is a common law generalization. Your community or state may have adopted specific statutes that give you greater rights. Again, your best bet is to check with an attorney or local low-cost legal service to find out more.

They have to give you 30 days notice.

When you gave them the intent to vacate in 60 days in writing, that's your official notice. When you went back and said you wanted to go month to month, Was there anything in writing? If not, I guess what happened was your earlier notice was still there and somebody didn't realize you wanted go month to month. Look at the most recent lease you signed with them and see what it says about notice to vacate. My guess is it probably says 2-4 weeks of notice. Are they giving you at least that much time? If they aren't, you can at least go to them and ask them to comply with that. Other than that, all you can is asking them to let you stay until you find somewhere else.

Whether it is legal or not is shaky round and would be best addressed by a real estate attorney. I cannot give legal advice and am not licensed to practice law in the state of texas HOWEVER I have had many years in property mangement, have gone to court on multiple occaasions, and will soon be getting my Texas real estate license.
That being said,
in Texas,
as a property manager I can lease an apartment for the end of the term BEFORE you give notice, if I am planning on giving you notice and there is plenty of time remaining to do so or AFTER I have received your notice of intent to move out. However, both parties are subject to gie the other X amount of days notice in writing should move out be imminent. X being a number agreed upon in your lease defaulting to 30 for TAA leases.

Also, verbal contracts or notices are hard to enforce in court. In other words, unless you rescinded your notice of intent to move out IN WRITING and got some sort of note back from them letting you knwo that they had not yet leased your unit, you might not have a leg to stand on in court.

I would suggest contacting your city's version of the Austin Tenant's Council to see what they can do for you or get a real estate awyer if you really want to fight it.

If you did not rescind your notice in writing, your options are VERY limited.