If you look at the map in HBHD for end of the 1st SW both Badlands and Lorkdal are both shown. At the end of the 2nd SW the area is still known as the Badlands Cluster but neither world is shown. As Badlands was settled prior to the RW, we can assume it does not need any advanced SL tech to be habitable. Lorkdal on the other hand may have needed advanced SL tech.
The most likely answer of what happened is that the TC abandoned it/could not support it due to tech decline as they cut off and abandoned a number of outlying worlds (almost the entire Brinton and Dumassas Unions). In that case pirates moved in and took over. (say like on Alphard)
The other option is that the worlds that the people of the Badlands simply told Taurus go to hell and leave us alone. I don't think this works as well as the worlds being abandoned due to lack of tech- in the various SBs we hear about numerous worlds being lost due to the loss of power plants and water purification systems. It also makes sense that the TC would concentrate it's efforts on the worlds closest to Taurus, as the loss of HPGs will make communications with outlying worlds very difficult.
I very much doubt the Badlands was taken over by the Periphery Battlemech Regiments, but given the location and nature of the region, I suspect that they use it as base of operations for the attacks against the SLDF.