Congressional Staff

During the time between now and when a replacement is elected via special election process, Weiner's staff will continue to operate under the supervision of the House clerk. His staffers will be able maintain some services for constituents, although they will have no authority, seniority, or voting rights on matters considered by the House. The special election process is expected to take about 3 to 6 months.

So, the answer is that they don't immediately lose their jobs. They have what amounts to a 3 to 6 month notice that the office is closing and they need to find new jobs.