You can apply for TPS while on F-1 status. Remember that TPS is temporary. As long as you comply with the conditions of your visa, you can keep your F-1 status, at the same time that you have TPS.
A person with TPS benefits is not required to attend school and may switch jobs at any time. The individual is not required to work and may choose from any employer that will hire. However, there are tradeoffs for giving up F-1 visa status.
The F-1 visa potentially provides a path to permanent resident status if the individual is able to obtain H1B status and then find an employer that is willing to sponsor the employee for a green card. If the individual's goal is to permanently immigrate to the United States, this may be the better option.
TPS is a temporary status that expires at the end of the designated period. DHS may or may not extend this period. If TPS is not extended, the individual will be required to depart the United States if he/she has no other valid status. If the individual's goal is short-term employment and to return to a home country, TPS may be a good solution.
Each case is different. Before applying for TPS, the individual should consult with an experienced immigration attorney who can give the situation more in-depth analysis.