Yes, someone who is a permanent resident in the United States can still travel to another country. Just because they have a green card does not mean they have to stay in the U.S. indefinitely.
For instance, maybe you moved to the United States years ago when you enrolled in college and had a student visa. You met a citizen who was also a college student, the two of you got married, and you were able to secure a green card.
If you want to go back to your home country to visit extended family members, you are allowed to do so. You are not going to lose your green card.
Potential complications
That being said, there are a few details to keep in mind. One is that the above applies to brief trips, but an extended trip could be more problematic.
As a rule of thumb, your trip should be under a year. If it lasts for more than a year, then you could have trouble re-entering the country. An extended absence can sometimes cause the government to say that you have abandoned your status or that you never intended to live in the U.S., and so your green card is being revoked.
There may be a case where you need to leave the country for more than a year. If so, one of the best ways to protect your green card is to apply for a reentry permit in advance, using Form I-131. Having this paperwork in your possession when you return can help you re-enter the country without issue.
Protecting your status
It is very natural that you would be concerned about losing your green card status, as it can be hard to obtain. To learn more about how to protect your status or what legal steps to take, it can be helpful to talk with an experienced immigration attorney.