Chile

Article 29 states:

If, because of temporary impediment, either for illness, absence from the territory or some other grave reason, the President of the Republic is unable to exercise his position, he will be substituted for, with the title of Vice President of the Republic, [by] the titular Minister to whom it corresponds, in accordance with the order of legal precedence. In default of the latter, the substitution will correspond to the titular Minister who follows [next] in [the] order of precedence and, in the default of all of them, the President of the Senate, the President of the Chamber of Deputies and the President of the Supreme Court, successively, will substitute for him. In case of vacancy in the position of President of the Republic, the substitution will be produced as in the cases of the preceding paragraph, and it will proceed to elect the successor in conformity with the rules of the following paragraphs. If the vacancy is produced less than two years before the next presidential election, the President will be elected by the Plenary Congress by an absolute majority of the Senators and Deputies in office. The election by Congress will be made within the ten days following the date of the vacancy; and the [person] elected will assume office within the following thirty days. If the vacancy occurs two years or more before the next presidential election, the Vice President, within the first ten days of his mandate, will convoke the citizens to presidential election for one hundred twenty days following the convocation, if that day corresponds to a Sunday. If it does not, it will be held on the Sunday immediately following. The President thus elected will assume his responsibilities [on] the tenth day following his proclamation. The President elected in conformity with any of the preceding paragraphs will remain in office until completing the term remaining of the [person] replaced, and cannot be presented as [a] candidate in the next presidential elections.

Article 53 states:

Exclusive attributions of the Senate are:…(7) To declare the incapacity of the President of the Republic or of the President-elect when a physical or mental impediment prevents him from the exercise of his functions; and to, declare likewise, when the President of the Republic [tenders his] resignation from his position, if the grounds that originate it are or [are] not well-founded and, in consequence, to accept it or reject it. In both cases, the Constitutional Tribunal must be previously heard…

Article 60 states:

…The Deputies and Senators may renounce their positions when they are affected by a grave illness that impedes them from carrying out [their functions] and the Constitutional Tribunal so qualifies [it].

Article 80 states:
The judges will remain in their positions during their good behavior... Notwithstanding the above, the judges will cease in their functions when becoming 75 years of age; or by resignation or [by] legal supervening incapacity…In all cases, the Supreme Court can declare, on the demand of the President of the Republic, on the request of an interested party, or of office, that judges have not had good conduct, and, after a report of the defendant and of the respective Court of Appeals, in such case, agree to his removal by the majority of the total number of its members. These agreements will be communicated to the President of the Republic for their fulfillment.

Article 89 states:

The National Attorney and the regional attorneys can only be removed by the Supreme Court, at the request of the President of the Republic, of the Chamber of Deputies, or of ten of its members, for incapacity, bad behavior or manifest negligence in the exercise of their functions…

Article 113 states:

…The regional councilor who during his exercise [of office] loses any of the requirements of eligibility or incurs in any of the disabilities, incompatibilities, incapacities or other causes of cessation that the constitutional organic law establishes[,] will cease in his office [cargo]…

Excerpts from the Political Constitution of the Republic of Chile (1980, last amended 2012)