Although the question stands for itself, I would like to know that if the answer has to be no then does any particular law forbids the existence of such forces; and if there are such forces then what are these and upon travelling under such forces in a closed loop where does the energy come from (as they are non conservative and non dissipative)?
Addendum: I would also highly appreciate it if someone could give an example of force fields which could be set up and left undisturbed by movement of particles under their influence. For example a charged non conducting fixed sphere provides an approximately fixed static field under which if particles move the cause is not disturbed. Since we know about induced electric field, but motion of charged particles under induced electric field, disturb its cause and then we have to supply more energy to maintain the field at original state.
I would hasten to add that although this would be highly appreciated, its not a necessity for the original question.