Can people who have broken the law and been in prison still be policemen or lawyers?

People who have received criminal punishment (imprisonment) for illegal crimes cannot be policemen. If it is a negligent crime, you can be a lawyer. You can't be a lawyer if you commit a crime on purpose.

Article 26 of the People's Police Law shall meet the following conditions:

(1) Persons who have reached the age of 18;

(2) Supporting the Constitution of People's Republic of China (PRC);

(3) Having good political and professional qualities and good conduct;

(4) Being in good health;

(5) Having graduated from high school or above;

(6) Volunteering in the work of the people's police.

One of the following circumstances, shall not serve as the people's police:

(1) Having received criminal punishment for committing a crime;

(2) Being expelled from public office.

Article 7 of the Lawyers Law An applicant shall not be issued a lawyer's practice certificate under any of the following circumstances:

(1) Having no or limited capacity for civil conduct;

(2) Having been subjected to criminal punishment, except for negligent crimes;

(3) Being expelled from public office or having his lawyer's practice certificate revoked.