LBB1 doesn't, but TTB and ST both reduce skills past the limit (sum of skill levels caps at sum of Int+Edu) to zeros, not no skills.So, I don't think MgT or LBB1 offer Lv 0 of the skill to anyone?
MGT 1e, you get level 0 in the whole service skills table on first term in a career. plus some background skills at 0.