To date, the hot Jupiter WASP-12 b has been the only planet with confirmed orbital decay. The late F-type host star has been hypothesized to be surrounded by a large structure of circumstellar material evaporated from the planet. We obtained two high-resolution spectral transit time series with CARMENES and extensively searched for absorption signals by the atomic species Na, H, Ca, and He using transmission spectroscopy, thereby covering the He I λ10833 Å triplet with high resolution for the first time. We apply SYSREM for atomic line transmission spectroscopy, introduce the technique of signal protection to improve the results for individual absorption lines, and compare the outcomes to those of established methods. No transmission signals were detected and the most stringent upper limits as of yet were derived for the individual indicators. Nonetheless, we found variation in the stellar Hα and He I λ10833 Å lines, the origin of which remains uncertain but is unlikely to be activity. To constrain the enigmatic activity state of WASP-12, we analyzed XMM-Newton X-ray data and found the star to be moderately active at most. We deduced an upper limit for the X-ray luminosity and the irradiating X-ray and extreme ultraviolet (XUV) flux of WASP-12 b. Based on the XUV flux upper limit and the lack of the He I λ10833 Å signal, our hydrodynamic models slightly favor a moderately irradiated planet with a thermospheric temperature of ≲12 000 K, and a conservative upper limit of ≲4 × 1012 g s−1 on the mass-loss rate. Our study does not provide evidence for an extended planetary atmosphere or absorption by circumstellar material close to the planetary orbit.