Back in 2013, U.S. Citizenship and Immigration Services (USCIS) set up a method meant to ease the way to a U.S. green card for unlawfully present spouses, parents, and ummarried minor children of U.S. citizen members of the U.S. military (current or past).
Called “parole in place” (or PIP), this new procedural avenue was meant to allow people who already qualified for a U.S. green card based on their family relationship to “adjust status”—that is, apply for lawful permanent residence or a green card—without leaving the United States, despite their past unlawful entry and stay.
The reason this was important was (as described in Adjustment of Status via "Parole in Place" for Family Members of U.S. Citizens in Military) that the majority of immigrating family members who entered the U.S. illegally (without a visa or other form of permission) will need to leave the U.S. for “consular processing” in order to complete their application for a U.S. green card. But when they get to the consulate, they might face a three- or ten-year bar upon return, as a penalty for their past unlawful presence.
This trap prevented many noncitizen family members of U.S. military servicepeople from applying for a green card in the past. (A so-called "provisional waiver" might help avoid problems at the consulate, but not everyone is able to prove the level of hardship that is required to be approved for the waiver.)
Now in 2017, however, the PIP policy faces an uncertain future. One of the executive orders issued by Donald J. Trump (the one titled “Executive Order: Border Security and Immigration Enforcement Improvements”) says that no form of parole should be granted on an across-the-board basis. Many analysts are concerned that this will spell the end of PIP.
(See, for example, this San Diego Tribune opinion piece, "Trump order drops protection for families of deployed military.")
It's important to realize that the Trump administration has not, as of this writing, definitively said that it would end PIP. Many types of parole exist--it's questionable whether the people who wrote the order even realized that this category existed and its importance for military families.
Nevertheless, if you are about to apply for PIP, consult an attorney before taking the risk of being arrested and deported.