Really? There must be some replacement who steps in though, no? Otherwise districts would have no representation, which seems unlikely.
> When vacancies happen in the Representation from any State, the Executive Authority thereof shall issue Writs of Election to fill such Vacancies.
- Article I, Section 2
For the Senate, the governor of the state may (per their legislative body's approval) make a temporary appointment and will also hold a special election:
> When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.
- Amendment XVII
https://www.archives.gov/founding-docs/constitution-transcri...
https://www.archives.gov/founding-docs/amendments-11-27#toc-...