The reason why the energy increases according to collapse theories, is that the collapse noise diffuses the particle, thus accelerating it. This is the same situation as in classical Brownian motion. And as for classical Brownian motion, this increase can be stopped by adding dissipative effects. Dissipative versions of the QMUPL, GRW and CSL model exist, where the collapse properties are left unaltered with respect to the original models, while the energy thermalizes to a finite value (therefore it can even decrease, depending on its initial value).