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There are a lot of different methods that can be used: nve/limit, soft potentials, energy minimization, and more. There is no guaranteed method, and depending on the situation, different approaches might be more useful than others. Read the LAMMPS manual for more details on how the different methods work.
As for “rebuilding” the system, that’s probably not very likely to work, as you’ll probably create another high-energy state. (That’s the default, unless your system is exceptionally simple.)