I may have an unpaid balance when I leave an extended stay hotel and wanted to know what legal steps they will take to collect on it?

Sue you in court... win, get writ of garnishment... seize bank account assets and or garnish you paycheck until the debt is paid. On top of wrecking your credit for 7 years until its collected. Few places will loan you a dime with a collection against you. Many employers won't hire you, your insurance rates will increase...

PS: It will be cheaper to pay what you owe now before that happens. Instead of guessing...call them and find out for sure.

...or garnish you paycheck ...

As I recall, paycheck garnishments are not allowed in Texas.