Final answer:
A practice where employees must join a union within a specified time or risk losing their jobs is called a union shop, part of union security agreements. The legality varies by state, and during disruptive strikes, a cooling-off period can be declared. Union membership in the U.S. has declined significantly over time.
Step-by-step explanation:
The practice referred to in the question is known as a union security agreement, specifically a type called a union shop. This type of agreement requires that employees join the union within a certain period of starting employment or maintain their membership as a condition of employment. The legality of such requirements can vary from state to state in the U.S., particularly due to right-to-work laws. Certain states allow all workers at a firm to be required to join a union as a condition of employment. Additionally, during a disruptive union strike, the president may declare a cooling-off period where workers are required to return to work temporarily while negotiations continue. In some professions, like law, membership in a professional organization, such as the American Bar Association, may be required. However, American union membership has declined significantly over the years due to various economic and legal factors.