You can run them on standards struts/dampers, generally as long as there are bump stops to prevent the dampers hitting full travel and bottoming out there will be no damage per se, but due to the harder spring rate there will be increased wear on them.
Most cars you see that are lower than standards will not be running any different dampers to standard (ie. standard travel), and realistically don't end up with shot suspension because of this. In an ideal world you'd run shorter stroke dampers as the suspension would have less travel with shorter/stiffer springs, and the dampers would also have a harder rebound rate to match the springs. Of course, this is simply in an ideal world and most people will just throw lower springs in and maybe put in a newer set of standard or slightly uprated dampers/struts.
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