Big Bend National Park and the nearby area is likely the safest US border area of any part of the continental US borders - safer than almost all of the US - CANADA border. I would certainly believe Big Bend is safer than the St. Clair River between Michigan and Canada.
Big Bend is about a hundred miles from nowhere in the US, almost double that from anywhere in Mexico.
It has always been one of the very lowest activity areas of the US - Mexico border as far as crossing - illegal or legal. Extremely low drug trafficking, almost never human trafficing.
There is one legal border crossing between Del Rio, TX and Persidio, TX - a distance of almost 300 miles along the river. That crossing is a BOAT at Boquillias near Rio Grande Village Campground in the National Park.
It takes near a hundred miles of unimproved dirt road in Mexico to get to the park river boundary.
Drug traffic activity is easily spotted by Border Patrol. Illegal crossings are very rare. People stand out in the area, and anyone trying to cross near Big Bend has over a hundred miles of desert to cross to get to possible farther transportation.
East near Del Rio is a much easier place to cross and disappear into the US. Persidio, TX is better, but very hard to avoid Border Patrol.
The emergency wildfire crew for the NP is Mexican residents of Boquillas. They have been known to turn in strangers who try to enter the US illegally.
Right now I'm sitting in Mercedes, TX - about 5 miles from the border, maybe 25 miles from Matamores - where I will not go.
We crossed into Mexico on Saturday at Nuevo Progresso, to buy drugs. Metformin, Losartin and a few other prescriptions for diabetes, blood pressure, thyroid. They were cheaper than the $10 co-pay of my retired US Navy health plans.
There are places in the US near the border where I will not go. More places in Mexico where I would not go.
Big Bend area is about the safest there is in my experience.