A cave formed by some form of ground movement.
The most common is due to landsliding in a jointed rock, leaving an open fissure cave parallel to the line of the hillside along the back of the slipped block.
Tectonic caves can form in any rock, as they do not depend on dissolution.
Well known examples are the windypit fissures of north-east Yorkshire, England some of which are hundreds of meters long and up to 60 m deep .
Glossary of Karst and Cave Terms
A tectonic cave is a secondary cave, but its formation has nothing to do with dissolution (corrosion) or erosion. The type of rock is almost irrelevant for the formation of this cave type. The main force for the cave genesis is a tectonic force, mechanical stress moving rocks. Tectonic caves can be formed by any geological force that causes rocks to move apart. In other words its a result of plate movements.
The most common tectonic caves are Talus caves, which are formed by rock slides and collapses. Less common are Fissure caves which are also formed by rock slides, but in a different way. The Neotectonic caves are formed by glacial processes an are typical for Scandinavian countries.
And finally there is a related process happening inside caves, which is thus generally interpreted as an aging process of caves. It is called breakdown and is the collapse of rock inside caves. It does not create caves but may change existng caves substacially.