Their should be some kind of option for a recall, or at the very least the people should vote them out of office when they come up for election, but yes they should be allowed to finish their term. This is part of how democracy works. People pick a politician and then they are stuck with that person.
Yes, leaders should be allowed to finish their terms of office regardless of how low their approval ratings drop. Most countries probably have ways to oust someone from office if they are doing a poor job. In the United States, Congress can impeach a president for committing a crime. The electorate also has a means to vote someone out of office. Both of these methods are difficult and rightfully so. A leader put in office through legal means should not be impeded in their quest to lead for whatever term they are given.
Yes, political leaders should be allowed to finish their terms even if their approval ratings drop below ten percent. It is the right of a democratic nation to call for the resignation or impeachment of a political leader deemed unfit or criminal, but approval rating alone should not be enough to remove a politician from office. That would undermine the stability of public office.
If the law of the country states that whatever leader is in charge for a certain period of time because the majority of voters put them in that position of power that I believe that they finish their term unless they commit some sort of crime. The people put him in that position in the first place so they only have themselves to blame.