When you're in the Sanctuary keep tipping Moxxi more than $10K each time.

If you do this enough time, she will give you a weapon. She might give it to you sooner if you tip her each time she stops talking to you.

When you get the weapon, you can then fast travel to another area of the game, then back to the Sanctuary.

If you do that and then keep tipping her, you'll get another weapon!

The two types of weapons she can give you are either a Corrosive or a Fire elemental submachine gun.