A mugger is a human monster in SLASH'EM. They are not randomly generated, but four of them appear in the shopping mall (if it exists), and one is guaranteed to appear in Grund's Stronghold. Despite what one might think from their source "mythology," they are not in fact able to steal your items.
The muggers in the Mall are not much of a threat, except inasmuch as one might find and use an attack wand or a highly enchanted weapon from a shop. This is relatively rare, however, and most of the time they are somewhat nonthreatening. They can be useful in other ways, however. First of all, they are one of very few easy sources of human corpses for sacrifice early on, if you are chaotic and wish to convert an altar with certainty. Also, since they like to collect items, they can be useful in stealing a few items from shops for you, which at the very least can then be sold back to the shopkeeper. For this reason, it is well worth it to make sure not to kill them in the shops in the mall, but rather wait for them to come outside, so the shopkeeper will no longer own whatever items they are carrying.