You can delete it from the database in table ow_base_avatar, you will first need to get the userid from the ow_base_user table first then find that value in the ow_base_avatar.
And then you will need to remove the actual image's from the ow_userfiles/themes/base/avatars there are three files
look for the user id in the file name, dont worry about the timestamp part of the file name just find the user id in three files
avatar_userid#
avatar_big_userid#
avatar_original_userid#
done.
Users cannot do that, they have to have something up there, avatar or something. There is a default "no pic" image if you have your avatar set to not required on reg but once they upload something, then thats it, they always have to have something from that point forward.
What you can do is
A. make an image in photoshop or paint that is a generic image 140 x 140
B. or look in your theme images folder and grab the "no pic" image,
give them a place to download that image and then they can upload it to their avatar.