Yes, if you have a student visa that allows you to attend a college or university in the United States, dropping out of that program could violate the terms of your visa and cause you to be out of status. This is true for either an F-1 or an M-1 visa.
Generally speaking, students need to be wary of taking a break for more than five months. If they are not enrolled in classes for a short time, such as when switching programs within the school or perhaps transferring to another university entirely, they can keep their status. But once they have exceeded the five-month deadline, they no longer legally qualify as a student under current immigration laws.
There are cases where students will be away from classes beyond this deadline, but want to return to school. In order to do so, they often have to apply for a new student visa. Their old visa can no longer be used because they have lost their status.
Would they have to leave the country?
It depends on whether they can achieve reinstatement of their status. The application for reinstatement needs to be filed with U.S. Citizenship and Immigration Services (USCIS). This is done using Form I-539. The student will likely also need to file Form I-20 through the Student and Exchange Visitor Information System (SEVIS).
In some cases, a student can have their status restored, and, as long as their original visa has not expired at that time, it can continue to be valid. However, if they are denied reinstatement, they lose their status. This often means that they immediately need to leave the country, and failing to do so could qualify as unlawful presence.
Much like a work visa, which does require employment in order for someone to keep their status, it is generally best for students to remain enrolled and actively taking classes as long as they are in the country on a student visa.
Exploring your options
If you are worried about your status, there are avenues to pursue, such as seeking a new visa, applying for reinstatement, adjusting your status or seeking a different type of visa. It is very important to know all of your options at this time, especially if you are facing the risk of deportation, and an experienced immigration attorney can help.