I was amused by the other suggestions, but as and worked out, the EUBAMчики are the EU customs officers operating on the frontier between Ukraine and Moldova, in a set-up known officially as the EU Border Assistance Mission, EUBAM for short.

points out that if it is a Russian slang word, it is more likely to be EUBAMшники than EUBAMчики. I confess that the subject came up over a dinner table in a crowded restaurant, so it is possible that I misheard; it’s also possible, as suggests, that it is Ukrainian rather than Russian slang, which I suppose might make a difference.