Sure. Proper grammar used to be: "If anyone here breaks the law, he may expect to pay the consequences."

Present more common usage: "If anyone here breaks the law, they may expect to pay the consequences."

"they" is incorrect grammar in that case...or at least, it certainly used to be.

Now, if one had been addressing a room of female students, let's say, one would have said: "If everyone will please open her test paper, we can begin now..."

But if one had addressed a room of both boys and girls, one would have said: "If everyone will please open his test paper..." or might have said "his or her test paper" in some cases, but usually just "his"

Now has become: "If everyone will please open their test paper..."

It's not a big deal, but there are times when it just doesn't sound right to me to say "they" or "their" when it used to be "his" or "her". "Everyone" means..."each single person". A single person is not "they".