Whether they are minors (under the age of 18) or adults, foreign nationals are expected to leave the United States at the end of any permitted stay under a nonimmigrant (temporary) visa. The exact date is usually shown on Form I-94, a card put into the person's passport upon entry to the United States, OR if you entered after April 2013, it will most likely be a form you can print out online from the Customs and Border Protection (CBP) website.
On the other hand, foreign-born minors don't face the same consequences for unlawful presence as adults do. They are exempt from becoming inadmissible for three or ten years based on unlawful presence of 180 days or more.
Are there any actual consequences when a minor overstays a nonimmigrant visa? Yes, with only limited exceptions, as addressed below.
When minors overstay a nonimmigrant visa, even if for only a few weeks, they can expect, just like all other visa holders must, that the visa will be automatically voided. (See I.N.A. § 222(g), 8 U.S.C. § 1202(g).)
If, for example, it were a multiple entry B-2 visa for visiting the United States as a tourist visitor, it would no longer be good for future trips. What's more, an overstay on one's record can make it difficult to obtain many other nonimmigrant visas or immigration benefits in the future, since U.S. immigration authorities will have to first be convinced that you will abide by the terms of your next visa.
A minor who is in the United States beyond the expiration date of a permitted stay under a nonimmigrant visa is at risk of being arrested by the immigration authorities and placed into removal proceedings. This is likely to lead to removal from the United States, under which circumstances the person will not be legally permitted to return for several years.
Without any exception for minors, people who have overstayed their nonimmigrant status are not allowed to change or extend their status from within the United States. For example, if you came to the United States on a visitor visa, stayed past the date on your I-94, and then were accepted by a U.S. college, you would not be able to apply to change to student (F-1) status.
You might be able to solve this problem by leaving the United States and applying for an F-1 visa though a U.S. consulate in your home country, but the consulate might hold your past overstay against you when considering whether to grant the visa. After all, the consulate has to be convinced that you'll return to your home country when your studies are over, and the past overstay doesn't bode well for this. (See Why You May Be Denied a U.S. Student Visa.)
In addition, people who've overstayed a visa are ineligible to adjust status to lawful permanent residence (get a green card from within the U.S.). The only exceptions are for immediate relatives of U.S. citizens (their spouse, parents, and minor unmarried children) and certain people who were "grandfathered in" under an old law, Section 245(i) of the Immigration and Nationality Act (I.N.A.), which allows for adjustment of status with the payment of a financial penalty.
A person over the age of 18 who accrues "unlawful presence" (for example, by overstaying a visa) of more than 180 days and who then leaves the U.S., is barred from reentering for three years. One who accrues unlawful presence of more than one year and then departs is barred from returning for ten years. (See Understanding the Three and Ten-Year Bars for Unlawful Presence.)
People in J-1 or F-1 status with I-94s that are designated "D/S" for "duration of status" are not affected by this law, unless USCIS has separately determined that they have overstayed their status.
As mentioned above, time spent as a minor does not count toward unlawful presence. However, as soon as you turn 18, the time starts adding up (and fast).
If you're thinking, "Well, it says this law applies only to people who leave the United States, so I simply won't leave, but will try to get a green card here," think again. Let's say someone wants to offer you a job and sponsor you for a green card. In this and most other cases (with an exception for if you became the immediate relative of a U.S. citizen or were grandfathered in under the old I.N.A. Section 245(i), someone who is in the United States unlawfully cannot apply for a green card without first leaving to attend an interview at a U.S. consulate in their home country. It is there, at the consular interview, that you may be penalized with a bar upon your return.
There is a waiver available, but it's not easy to qualify for. (See Staying in the U.S. With The I-601A Provisional Waiver of Inadmissibility.) You'd in all likelihood need a lawyer's help.
If you or a member of your family has overstayed a U.S. visa and you are unsure what result this will have on future applications for visas or green cards, it would be worth consulting with an immigration attorney. After carefully analyzing your case, the attorney might point out possibilities or exceptions of which you were not aware.