"entrenched themselves" is a grammatically correct phrase which can be used in written English.
Example sentence: The troops entrenched themselves behind the mountains and prepared for battle.
The Taliban have firmly entrenched themselves in the trade.
The Confederates had entrenched themselves well on a hill near a bend in the Oostanaula River.
Confederate troops under Lee at Cold Harbor entrenched themselves in defensive positions behind earthworks.
They've entrenched themselves in the borough and engaged themselves with the city.
Despite their flaws, the Bulldogs have entrenched themselves in the national conversation again this season.
The Egyptians held Gaza, and the Syrians entrenched themselves in the Golan Heights overlooking Galilee.
View Photo Gallery: Demonstrators have entrenched themselves in Freedom Plaza and McPherson Square downtown.
Regulation often starts with good intentions, but there are many industries that have entrenched themselves behind unnecessary regulation, too.
Ferdinand, on the other hand, failed in his attempt to take Ofen (Hungarian: Buda), where the Turks had entrenched themselves.
By now, racist and antisemitic Pepe the Frog images have entrenched themselves in the iconography of the alt right.
