Yes, the packers could move clothes. There are full-service moves that you could opt for, in which the movers will take care of anything and everything. In the full-time service, the movers will help you pack and
unpack your stuff. The packers and movers will pack the clothes in various ways. Some of them are,
In a box- they will line the bottom of the box with packaging paper and stack up the folded clothes in the box.
Drawer- they could also put the folder box into the drawer and then glide the drawer back into the furnace.