Would a doctor be considered a false witness if they provided a medical certificate justifying a person's absence from work or study, knowing that the reason for absence may not always be illness, and in some cases, the medical certificate is the only solution to prevent a head of household from being fired from their job or a student from being expelled from their studies?

A medical certificate stating that its holder is unable to work due to illness, if it does not conform to reality, is a false testimony and is not permissible. One who is absent from work must inform the officials of his true excuse. If they do not accept it, he should not lie or resort to false testimony. Rather, he should be patient and seek his reward from Allah, for: "And whoever fears Allah – He will make for him a way out And will provide for him from where he does not expect."