It happened to me. It's what livesoft says.
It's no biggy, just a nuisance in filling out the tax forms. And of course you ultimately pay back the tax break you temporarily got on the excess contribution. I forget the sequence of events, but basically you just sit around and stuff comes in the mail and you just follow all the directions about what to do that pertain to a 1099-R form.
As I recall it goes something like this. You contribute too much in year X. In year X + 1, the 401(k) provider spits your excess contribution back to you by mailing you a check. That check is taxable income in year X + 1, and early in X + 2 you get a 1099-R form declaring it, and you write it in some appropriate box on your year X + 1 tax forms and pay the taxes. Or something like that.
It's not considered naughty or anything. It's all routine, you just save the stuff you get in the mail and follow directions. And if you're not quite sure what to do, there aren't any nuances in interpretation, it's just the sort of thing where you can call up the IRS at 1-800-829-1040 and they'll tell you step A, step B, step C.
The challenge is to figure out how much it's safe to contribute in future years if you don't want to go through the rigamarole again. It has to be a guess, HR isn't going to be able to tell you the exact number in advance.
Your wife
might consider suggesting to management that they be less stingy with the 401(k) match and get more employees contributing... and, of course, if she doesn't have a Roth IRA already, she should get one, and if she cuts back on her 401(k) contributions to avoid overcontributing she should contribute correspondingly more to the Roth.
Ah, 'tis a
hard, hard life for HCE's.
P.S. Also, if it hasn't happened to her already... she wants to be circumspect about mentioning the increase in her paycheck that she'll get when she maxes out her Social Security contribution for the year and they quit deducting it. Don't do what I did, which was to blurt out to a colleague, "Hey, this is funny, my paycheck is a little larger this month... is yours? do you know why?" because, of course, by disclosing the month in which you max out your Social Security contribution you are also disclosing your income.

Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.