Who can be impeached?
The Constitution allows only two penalties as a result of impeachment: removal from office, and being banned from holding future federal office.
Technically, it is probably the case that Congress could impeach a President who had left office in order to prevent them from holding future office in the Federal government. This would not only prevent a one-term president from returning to seek another term at a later time, but would prevent a former president from running for Congress or serving in the cabinet of a future president or as a federal judge or Supreme Court justice.
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Article II, Section 4 of the Constitution says, "The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other High Crimes and Misdemeanors."
To date, two federal judges have been impeached and removed from office based on charges of bribery. No federal official has ever faced impeachment based on charges of treason. All other impeachment proceedings held against federal officials, including three presidents, have been based on charges of “high crimes and misdemeanors.”