In Teas the law allows you to apply for homestead exemptions on the home you call your principal residence.
ONLY a homeowner's principal place of residence qualifies for a homestead exemption. To qualify for the exemption your home must meet the definition of a residence homestead: The home's owner must be an individual (for example: not a corporation or other business entity) and use the home as his or her principal residence on January 1 of the tax year. Therefore, she can't apply for this year. She can apply this year for an exemption effective January 1st of 2017.
If you are age 65 or older, or disabled, the January 1 ownership and residency are not required for the age 65 or disabled homestead exemption.
If your estranged spouse does seek a homestead exemption on her new home, she'll potentially be breaking the law.
I suggest you avoid commenting on this unless she asks. Your home wouldn't lose it's current exemption by virtue of her illicit actions. If you do divorce, she could then apply for the exemption.
Last comment, Texas recognizes marriages, and has no legal separation. You're married, you're divorced, which is the same as being single. Separation means nothing in the Texas legal system.