The short answer to this question is no. Once someone has obtained a Green Card (permanent residency) their status cannot be taken away just because they have gotten a divorce.
There are a couple of situations where a Green Card holder’s status as a permanent resident might be at risk if they get a divorce, but the U.S. does consider the rights of the people involved and does not summarily deport immigrants who have gotten divorced.
Divorce During the Conditional Green Card Period
Immigrants who receive a green card through marriage are initially given a conditional Green Card. This document is in many ways the same as a regular Green Card, the primary difference being that a conditional Green Card only lasts for two years instead of ten.
In order to switch from a conditional (two-year) Green Card to a regular (10-year) Green Card, permanent residents have to file Form I-751. It is a common mistake for conditional Green Card holders to think that they just need to renew their Green Card with Form I-90, but this is not the case at all. Once the two-year conditional Green Card period has passed, permanent residents have to use Form I-751 to get a new Green Card.
The reason for why there is even such a thing as a conditional Green Card is to prevent marriage fraud, specifically marriages-of-convenience, which are marriages entered into in order to obtain immigration benefits.
The United States (and most other countries) does not allow people to immigrate based on a marriage whose only purpose is to help someone immigrate.
The two-year conditional period exists to ensure that immigrants who come to the U.S. aren’t doing so fraudulently.
A divorce during this two-year period may be seen as suspicious, but there are still ways to establish that the marriage was real, that a divorce is necessary and for the immigrant to keep their Green Card if it is necessary.
Once someone gets a permanent resident card (Green Card), they do not lose their status unless the U.S. government discovers that the Green Card was obtained through fraud.
Related Article: Remove Conditions on Permanent Residence Based on Marriage