Immigrant Green Card holders must live in the United States to maintain their permanent resident status, otherwise they may lose their residence, however, there are certain exceptions.
One of the requirements to maintain legal permanent residence and subsequently be able to apply for US citizenship through naturalization is to live in the United States continuously and not leave the country for long periods of time. Permanent residents can leave the country for work or tourism, but only for short periods of time, without affecting their status.
However, there are options for permanent residents to live in Mexico or Canada without affecting their status in any way or having to give up their benefits. The Permanent Resident in Commuter Status or permanent resident in traveler status, is an exception available to certain residents of Canada and Mexico, which allows them to live in those countries while working. in United States. In addition, it is reversible, that is, they can return to permanent legal residence when they no longer need this traveler status.

In order to maintain and strengthen commercial and business ties with Mexico and Canada, US immigration laws offer this exception for residents who live in these countries, but work in the United States. There are two types of commuter status: for people who regularly travel to the United States, but live in Mexico or Canada, and for people who work seasonally for extended periods.
To identify residents with this status, the back of their Green Card reads the legend
“C2”, instead of the “C1” shown on Green Cards for permanent residents.
However, this status has its limitations and does not offer the same opportunities as a standard permanent residence status. For example, a resident with commuter status is not eligible to apply for naturalized citizenship until they return to standard resident status. You also cannot sponsor a family member for a Green Card.
In addition, in order to prove your status as a worker in the United States and residency in Canada or Mexico, you must appear at a port of entry every six months to complete Form I-178 and show the corresponding evidence.
To return to the standard permanent residence it is necessary to present the I-90 form, for the application or replacement of permanent residence card: https://www.uscis.gov/es/i-90.
Cabe mencionar que este estatus puede ser prolongado siempre y cuando el individuo presente pruebas de que ha trabajado continuamente en Estados Unidos por al menos 90 días durante el último año.