Squatter's rights, also known as adverse possession, are sometimes afforded to parties who have used a property openly and without objection from the actual owner for a set number of years, which varies by state. In your case, the property in question is a strip of land where the neighbors erected a gate and fence. This type of thing is often done when the owners, such as your parents, aren't on hand to challenge it. I might add there is a loophole in Texas state law that has given latitude to some squatters to try to claim entire homes in recent years. Most of these squatters, I'm pleased to note, have been foiled by court orders and extricated.
Your case is simpler. From the looks of it, your parents weren't around to witness the construction because they were disabled and even institutionalized for treatment. Normally, the real owners have five years to 10 years, depending on circumstances, to recover property that's used or held under adverse possession. However, if the original property owners suffered from legal disabilities such as your parents at the time squatters made their move, state statutes "toll" (stop or suspend) the countdown until those disabilities are removed or 25 years pass. So the law is on your family's side.
That doesn't mean the gate and fence can be immediately torn down. Sometimes such an encroachment is an honest mistake resulting from a bad survey, contractor error or a miscommunication in the past between neighboring parties. Other times, it's deliberate. Of course, I wouldn't blame you for suspecting that the departure of your parents may have bolstered the neighbors' courage in this case.
First off, you can request in writing that your neighbors remove the fence and gate. If the neighbors dispute the line, you may have to go to the local township or county office and pull the property survey, then check it against the property lines. You may even have to order a new survey if there's ambiguity, and that could be costly (more than $1,000 on a large rural property). Here, you could offer to split the survey's costs with the neighbor and agree beforehand to abide by the results.
If it does turn out that your neighbors' construction is on your folks' property and they won't budge, you can offer to sell the disputed land, assuming it won't affect the marketability of, or access to, your parents' land. If the neighbors balk again, then ask them in writing to move the construction to their property. If that fails, you may be entitled to carefully remove it yourself -- but be very cautious on this one. Alas, you may have to consult with an attorney to determine what statutes allow you to do.
As you can imagine, that road could get rocky and costly. It's always best to work these things out civilly if at all possible. Good luck!
Ask the adviser
To ask a question of the Real Estate Adviser, go to the "Ask the Experts" page and select "Buying, selling a home" as the topic. Read more Real Estate Adviser columns and more stories about mortgages.